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1

Q-Reflexive Banach spaces  

CERN Multimedia

Let $E$ be a Banach space and, for any positive integer $n$, let ${\\cal P}(^nE)$ denote the Banach space of continuous $n$-homogeneous polynomials on $E$. Davie and Gamelin showed that the natural extension mapping from ${\\cal P}(^nE)$ to ${\\cal P}(^nE^{\\ast\\ast})$ is an isometry into the latter space. Here, we investigate when there is a natural isomorphism between ${\\cal P}(^nE)^{\\ast\\ast}$ and ${\\cal P}(^nE^{\\ast\\ast})$. Among other things, we show that if $E$ satisfies: \\break (a) no spreading model built on a normalised weakly null sequence has a lower $q$-estimate for any $q < \\infty,$ (b) $E^{\\ast}$ has RNP, and (c) $E^{\\ast}$ has the approximation property, then ${\\cal P}(^nE)$ has RNP for every $n$. Moreover, if $E$ satisfies (a) and is such that $E^{\\ast\\ast}$ has both the RNP and the approximation property, then ${\\cal P}(^nE)^{\\ast\\ast}$ and ${\\cal P}(^nE^{\\ast\\ast})$ are isomorphic for every $n$. We also exhibit a quasi-reflexive Banach space $E$ for which ${\\cal P}(^nE)^{\\ast\\ast}$ and ${\\cal...

Aron, R M; Aron, Richard M.; Dineen, Sean

1994-01-01

2

Q-Reflexive Banach spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Let $E$ be a Banach space and, for any positive integer $n$, let ${\\cal P}(^nE)$ denote the Banach space of continuous $n$-homogeneous polynomials on $E$. Davie and Gamelin showed that the natural extension mapping from ${\\cal P}(^nE)$ to ${\\cal P}(^nE^{\\ast\\ast})$ is an isometry into the latter space. Here, we investigate when there is a natural isomorphism between ${\\cal P}(^nE)^{\\ast\\ast}$ and ${\\cal P}(^nE^{\\ast\\ast})$. Among other things, we show that if $E$ satisfies: ...

Aron, Richard M.; Dineen, Sean

1994-01-01

3

Uniform embeddings of bounded geometry spaces into reflexive Banach space  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We show that every metric space with bounded geometry uniformly embeds into an explicit reflexive Banach space (a direct sum of l^p spaces). In the case of discrete groups we show the analogue of a-T-menability. That is, we construct a metrically proper affine isometric action on this Banach space.

Brown, Nathanial; Guentner, Erik

2003-01-01

4

Banach space properties forcing a reflexive amenable Banach algebra to be trivial  

Digital Repository Infrastructure Vision for European Research (DRIVER)

It is an open problem whether an infinite-dimensional amenable Banach algebra exists whose underlying Banach space is reflexive. We give sufficient conditions for a reflexive, amenable Banach algebra to be finite-dimensional (and thus a finite direct sum of full matrix algebras). If $A$ is a reflexive, amenable Banach algebra such that for each maximal left ideal $L$ of $A$ (i) the quotient $A / L$ has the approximation property and (ii) the canonical map from $A \\check{\\oti...

Runde, Volker

2002-01-01

5

A universal reflexive space for the class of uniformly convex Banach spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We show that there exists a separable reflexive Banach space into which every separable uniformly convex Banach space isomorphically embeds. This solves a problem of J. Bourgain. We also give intrinsic characterizations of separable reflexive Banach spaces which embed into a reflexive space with a block $q$-Hilbertian and/or a block $p$-Besselian finite dimensional decomposition.

Odell, E.; Schlumprecht, Th

2005-01-01

6

Best Proximity Points of Cyclic ?-Contractions on Reflexive Banach Spaces  

Directory of Open Access Journals (Sweden)

Full Text Available We provide a positive answer to a question raised by Al-Thagafi and Shahzad (Nonlinear Analysis, 70 (2009, 3665-3671 about best proximity points of cyclic ?-contractions on reflexive Banach spaces.

N. Shahzad

2010-01-01

7

Best Proximity Points of Cyclic -Contractions on Reflexive Banach Spaces  

Directory of Open Access Journals (Sweden)

Full Text Available We provide a positive answer to a question raised by Al-Thagafi and Shahzad (Nonlinear Analysis, 70 (2009, 3665-3671 about best proximity points of cyclic -contractions on reflexive Banach spaces.

Shahzad N

2010-01-01

8

Fixed point theorem for reflexive Banach spaces and uniformly convex non positively curved metric spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

This article generalizes the work of Ballmann and \\'Swiatkowski to the case of Reflexive Banach spaces and uniformly convex Busemann spaces, thus giving a new fixed point criterion for groups acting on simplicial complexes.

Oppenheim, Izhar

2012-01-01

9

Some fixed point theorems in fuzzy reflexive Banach spaces  

International Nuclear Information System (INIS)

In this paper, we first show that there are some gaps in the fixed point theorems for fuzzy non-expansive mappings which are proved by Bag and Samanta, in [Bag T, Samanta SK. Fixed point theorems on fuzzy normed linear spaces. Inf Sci 2006;176:2910-31; Bag T, Samanta SK. Some fixed point theorems in fuzzy normed linear spaces. Inform Sci 2007;177(3):3271-89]. By introducing the notion of fuzzy and ?- fuzzy reflexive Banach spaces, we obtain some results which help us to establish the correct version of fuzzy fixed point theorems. Second, by applying Theorem 3.3 of Sadeqi and Solati kia [Sadeqi I, Solati kia F. Fuzzy normed linear space and it's topological structure. Chaos, Solitons and Fractals, in press] which says that any fuzzy normed linear space is also a topological vector space, we show that all topological version of fixed point theorems do hold in fuzzy normed linear spaces.

2009-09-15

10

On the surjectivity properties of perturbations of maximal monotone operators in non-reflexive Banach spaces  

CERN Document Server

We are concerned with surjectivity of perturbations of maximal monotone operators in non-reflexive Banach spaces. While in a reflexive setting, a classical surjectivity result due to Rockafellar gives a necessary and sufficient condition to maximal monotonicity, in a non-reflexive space we characterize maximality using a ``enlarged'' version of the duality mapping, introduced previously by Gossez.

Alves, M Marques

2008-01-01

11

On extension results for n-cyclically monotone operators in reflexive Banach spaces  

CERN Multimedia

In this paper we provide some extension results for n-cyclically monotone operators in reflexive Banach spaces by making use of the Fenchel duality. In this way we give a positive answer to a question posed by Bauschke and Wang in [4].

Bot, Radu Ioan

2009-01-01

12

Convergence theorems for common fixed points for finite families of nonexpansive mappings in reflexive Banach spaces  

International Nuclear Information System (INIS)

Let E be a real reflexive Banach space with uniformly Gateaux differentiable norm. Let K be a nonempty closed convex subset of E. Suppose that every nonempty closed convex bounded subset of K has the fixed point property for nonexpansive mappings. Let T1, T2, ..., TN be a family of nonexpansive self-mappings of K, with F := intersectioni=1N Fix(Ti) ? 0, F = Fix(TNTN-1... T1) = Fix(T1TN ... T2) = ... Fix(TN-1TN-2... T1TN). Let { ?n} be a sequence in (0, 1) satisfying the following conditions: C1 : lim ?n 0; C2 : ? ?n = ? . For a fixed ? element of (0, 1), define Sn : K ? K by Snx := (1 - ? )x + ?Tnx for all x element of K where Tn = Tn mod N. For arbitrary fixed u, x0 element of K, let B := { x element of K : TNTN-1... T1x ?x+(1- ?)u, for some ? > 1} be bounded and let the sequence {xn} be defined iteratively by xn+1 ?n+1u + (1 - ?n+1 )Sn+1xn, for n ? 0. Assume that lim n?? vertical bar vertical bar Tnxn - Tn+1 xn vertical bar vertical bar = 0. Then, {xn} converges strongly to a common fixed point of the family T1, T2, ..., TN. Convergence theorem is also proved for non-self maps. (author)

2007-01-01

13

A Representation of Stable Banach Spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We show that any separable stable Banach space can be represented as a group of isometries on a separable reflexive Banach space, which extends a result of S. Guerre and M. Levy. As a consequence, we can then represent homeomorphically its space of types.

Chaatit, Fouad

1996-01-01

14

A uniformly convex hereditarily indecomposable Banach space  

Digital Repository Infrastructure Vision for European Research (DRIVER)

A {\\em hereditarily indecomposable (or H.I.)} Banach space is an infinite dimensional Banach space such that no subspace can be written as the topological sum of two infinite dimensional subspaces. As an easy consequence, no such space can contain an unconditional basic sequence. This notion was first introduced in 1993 by T.Gowers and B.Maurey, who constructed the first known example of a hereditarily indecomposable space. Gowers-Maurey space is reflexive, however it is not...

Ferenczi, Valentin

1995-01-01

15

Nonmeasurability in Banach spaces  

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We show that for a $\\sigma $-ideal $\\ci$ with a Steinhaus property defined on Banach space, if two non-homeomorphic Banach with the same cardinality of the Hamel basis then there is a $\\ci$ nonmeasurable subset as image by any isomorphism between of them. Our results generalize results from [2

Ralowski, Robert

2010-01-01

16

Ergodic Banach Spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We show that any Banach space contains a continuum of non isomorphic subspaces or a minimal subspace. We define an ergodic Banach space $X$ as a space such that $E_0$ Borel reduces to isomorphism on the set of subspaces of $X$, and show that every Banach space is either ergodic or contains a subspace with an unconditional basis $ which is complementably universal for the family of its block-subspaces. We also use our methods to get uniformity results; for example, in combina...

Ferenczi, Valentin; Rosendal, Christian

2003-01-01

17

Subprojective Banach spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

A Banach space $X$ is called subprojective if any of its infinite dimensional subspaces $Y$ contains a further infinite dimensional subspace complemented in $X$. This paper is devoted to systematic study of subprojectivity. We examine the stability of subprojectivity of Banach spaces under various operations, such us direct or twisted sums, tensor products, and forming spaces of operators. Along the way, we obtain new classes of subprojective spaces.

Oikhberg, Timur; Spinu, Eugeniu

2014-01-01

18

Topological duals of Banach spaces as Banach algebras and applications  

International Nuclear Information System (INIS)

Banach algebra structures on the topological dual X* of a Banach space X are defined, and some algebraic and topological properties of such Banach algebras are studied. In this paper, on the second dual space X** of a Banach space X, different products, each of which turns X** into an associative Banach algebra which satisfies similar properties are also defined. 13 refs

1991-01-01

19

Interpolating hereditarily indecomposable Banach spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

It is shown that every Banach space either contains $\\ell ^1$ or it has an infinite dimensional closed subspace which is a quotient of a H.I. Banach space.Further on, $L^p(\\lambda )$, $1Banach space.

Argyros, Spiros A.; Felouzis, V.

1997-01-01

20

Strongly adequate functions on Banach spaces  

CERN Document Server

The notion of adequate function has been recently introduced in order to characterize the essentially strictly functions on a reflexive Banach space among the weakly lower semicontinuous ones. In this paper we reinforce this concept and show that a lower semicontinuous function is essentially firmly subdifferentiable if and only if it is strongly adequate.

Volle, Michel

2012-01-01

 
 
 
 
21

Multipliers of Banach valued weighted function spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We generalize Banach valued spaces to Banach valued weighted function spaces and study the multipliers space of these spaces. We also show the relationship between multipliers and tensor product of Banach valued weighted function spaces.

Serap ztop

2000-01-01

22

On unconditionally saturated Banach spaces  

CERN Document Server

We prove a structural property of the class of unconditionally saturated separable Banach spaces. We show, in particular, that for every analytic set $\\aaa$, in the Effros-Borel space of subspaces of $C[0,1]$, of unconditionally saturated separable Banach spaces, there exists an unconditionally saturated Banach space $Y$, with a Schauder basis, that contains isomorphic copies of every space $X$ in the class $\\aaa$.

Dodos, Pandelis

2008-01-01

23

Nonwandering operators in Banach space  

Directory of Open Access Journals (Sweden)

Full Text Available We introduce nonwandering operators in infinite-dimensional separable Banach space. They are new linear chaotic operators and are relative to hypercylic operators, but different from them. Firstly, we show some examples for nonwandering operators in some typical infinite-dimensional Banach spaces, including Banach sequence space and physical background space. Then we present some properties of nonwandering operators and the spectra decomposition of invertible nonwandering operators. Finally, we obtain that invertible nonwandering operators are locally structurally stable.

Lixin Tian

2005-01-01

24

BANACH SPACE VALUED POTENTIAL TRANSFORM  

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Full Text Available This paper studies different testing function spaces of Gelfand-Shilov type for the Banach space valued generalized Potential transform. The topological properties of these spaces are discussed. Different operators and their continuity is also discussed. The Analyticity theorem and Inversion theorem for Banach space valued distributional Potential Transform are also proved.

NANDA D. SAHU

2011-06-01

25

Dynamical entropy in Banach spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We introduce a version of Voiculescu-Brown approximation entropy for isometric automorphisms of Banach spaces and develop within this framework the connection between dynamics and the local theory of Banach spaces discovered by Glasner and Weiss. Our fundamental result concerning this contractive approximation entropy, or CA entropy, characterizes the occurrence of positive values both geometrically and topologically. This leads to various applications; for example, we obtai...

Kerr, David; Li, Hanfeng

2004-01-01

26

Tightness of Banach spaces and Baire category  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We prove several dichotomies on linear embeddings between Banach spaces. Given an arbitrary Banach space X with a basis, we show that the relations of isomorphism and bi-embedding are meager or co-meager on the Polish set of block-subspaces of X. We relate this result with tightness and minimality of Banach spaces. Examples and open questions are provided.

Ferenczi, Valentin; Godefroy, Gilles

2011-01-01

27

Existence of zeros for operators taking their values in the dual of a Banach space  

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Full Text Available Using continuous selections, we establish some existence results about the zeros of weakly continuous operators from a paracompact topological space into the dual of a reflexive real Banach space.

Biagio Ricceri

2004-08-01

28

Existence of zeros for operators taking their values in the dual of a Banach space  

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Full Text Available Using continuous selections, we establish some existence results about the zeros of weakly continuous operators from a paracompact topological space into the dual of a reflexive real Banach space.

Ricceri Biagio

2004-01-01

29

On nonatomic Banach lattices and Hardy spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We are interested in the question when a Banach space $X$ with an unconditional basis is isomorphic (as a Banach space) to an order-continuous nonatomic Banach lattice. We show that this is the case if and only if $X$ is isomorphic as a Banach space with $X(\\ell_2)$. This and results of J. Bourgain are used to show that spaces $H_1(\\bold T^n)$ are not isomorphic to nonatomic Banach lattices. We also show that tent spaces introduced in \\cite{4} are isomorphic to Rad $H_1$.

Kalton, Nigel J.; Wojtaszczyk, P.

1992-01-01

30

On holomorphic Banach vector bundles over Banach spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We show, e.g., that a holomorphic Banach vector bundle over a pseudoconvex open subset of, say, Hilbert space is holomorphically trivial if it is continuously trivial. Some applications are also given.

Patyi, Imre

2005-01-01

31

Strong convergence of a monotone projection algorithm in a Banach space.  

Science.gov (United States)

In this paper, a common solution problem is investigated based on a Bregman projection. Strong convergence of the monotone projection algorithm for monotone operators and bifunctions is obtained in a reflexive Banach space. PMID:24348187

Lv, Songtao

2013-01-01

32

Coarse embedding into uniformly convex Banach space  

Digital Repository Infrastructure Vision for European Research (DRIVER)

In this paper, we study the coarse embedding into Banach space. We proved that under certain conditions, the property of embedding into Banach space can be preserved under taking the union the metric spaces. For a group $G$ strongly relative hyperbolic to a subgroup $H$, we proved that if $H$ admits a coarse embedding into a uniformly convex Banach space, so is $B(n)=\\{g\\in G|\\abs{g}_{S\\cup\\mathscr{H}}\\leq n\\}$.

Ren, Qinggang

2011-01-01

33

Superreflexivity and J-convexity of Banach spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

A Banach space X is superreflexive if each Banach space Y that is finitely representable in X is reflexive. Superreflexivity is known to be equivalent to J-convexity and to the non-existence of uniformly bounded factorizations of the summation operators S_n through X. We give a quantitative formulation of this equivalence. This can in particular be used to find a factorization of S_n through X, given a factorization of S_N through [L_2,X], where N is `large' compared to n.

Wenzel, Joerg

1997-01-01

34

Properties and , Embeddings in Banach Spaces with 1-Unconditional Basis and  

Directory of Open Access Journals (Sweden)

Full Text Available We will use Garca-Falset and Llorns Fuster's paper on the AMC-property to prove that a Banach space that embeds in a subspace of a Banach space with a 1-unconditional basis has the property AMC and thus the weak fixed point property. We will apply this to some results by Cowell and Kalton to prove that every reflexive real Banach space with the property and its dual have the and that a real Banach space such that is sequentially compact and has has the .

Fetter Helga

2010-01-01

35

Homogenous Banach spaces on the unit circle  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We prove that a homogeneous Banach space on the unit circle T can be embedded as a closed subspace of a dual space [Xi]* contained in the space of bounded Borel measures on T in such a way that the map --> [Xi]* defines a bijective correspondence between the class of homogeneous Banach spaces on T and the class of prehomogeneous Banach spaces on T. We apply our results to show that the algebra of all continuous functions on T is the only homogeneous Banach algebra on T in...

Pedersen, Thomas Vils

2000-01-01

36

Boundaries for Banach spaces determine weak compactness  

Digital Repository Infrastructure Vision for European Research (DRIVER)

A boundary for a Banach space is a subset of the dual unit sphere with the property that each element of the Banach space attains its norm on an element of that subset. Trivially, the pointwise convergence with respect to such a boundary is coarser than the weak topology on the Banach space. Godefroy's Boundary Problem asks whether nevertheless both topologies have the same bounded compact sets. This paper contains the answer in the positive.

Pfitzner, Hermann

2008-01-01

37

Regularization methods in Banach spaces  

CERN Document Server

Regularization methods aimed at finding stable approximate solutions are a necessary tool to tackle inverse and ill-posed problems. Usually the mathematical model of an inverse problem consists of an operator equation of the first kind and often the associated forward operator acts between Hilbert spaces. However, for numerous problems the reasons for using a Hilbert space setting seem to be based rather on conventions than on an approprimate and realistic model choice, so often a Banach space setting would be closer to reality. Furthermore, sparsity constraints using general Lp-norms or the B

Schuster, Thomas; Hofmann, Bernd; Kazimierski, Kamil S

2012-01-01

38

On Quasihyperbolic Geodesics in Banach Spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We study properties of quasihyperbolic geodesics on Banach spaces. For example, we show that in a strictly convex Banach space with the Radon-Nikodym property, the quasihyperbolic geodesics are unique. We also give an example of a convex domain $\\Omega$ in a Banach space such that there is no geodesic between any given pair of points $x, y \\in \\Omega\\,.$ In addition, we prove that if $\\mathrm{X}$ is a uniformly convex Banach space and its modulus of convexity is of a power t...

Rasila, Antti; Talponen, Jarno

2013-01-01

39

Quotients of Banach spaces and surjectively universal spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We characterize those classes $\\mathcal{C}$ of separable Banach spaces for which there exists a separable Banach space $Y$ not containing $\\ell_1$ and such that every space in the class $\\mathcal{C}$ is a quotient of $Y$.

Dodos, Pandelis

2010-01-01

40

Characterizing R-duality in Banach spaces  

DEFF Research Database (Denmark)

R-duals of certain sequences in Hilbert spaces were introduced by Casazza, Kutyniok and Lammers in 2004 and later generalized to Banach spaces by Xiao and Zhu. In this paper we provide some characterizations of R-dual sequences in Banach spaces.

Christensen, Ole

2013-01-01

 
 
 
 
41

On $c_0$-saturated Banach spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

A Banach space E is c_0-saturated if every closed infinite dimensional subspace of E contains an isomorph of c_0. A c_0-saturated Banach space with an unconditional basis which has a quotient space isomorphic to l^2 is constructed.

Leung, Denny H.

1992-01-01

42

A Gaussian Radon Transform for Banach Spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We develop a Radon transform on Banach spaces using Gaussian measure and prove that if a bounded continuous function on a separable Banach space has zero Gaussian integral over all hyperplanes outside a closed bounded convex set in the Hilbert space corresponding to the Gaussian measure then the function is zero outside this set.

Holmes, Irina; Sengupta, Ambar N.

2012-01-01

43

Isometric embeddings of compact spaces into Banach spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We show the existence of a compact metric space $K$ such that whenever $K$ embeds isometrically into a Banach space $Y$, then any separable Banach space is linearly isometric to a subspace of $Y$. We also address the following related question: if a Banach space $Y$ contains an isometric copy of the unit ball or of some special compact subset of a separable Banach space $X$, does it necessarily contain a subspace isometric to $X$? We answer positively this question when $X$ ...

Dutrieux, Yves; Lancien, Gilles

2008-01-01

44

Nonreflexive Banach SSD spaces  

CERN Document Server

In this paper, we unify the theory of SSD spaces, part of the theory of strongly representable multifunctions, and the theory of the equivalence of various classes of maximally monotone multifunctions.

Simons, Stephen

2008-01-01

45

On Peano's theorem in Banach spaces  

CERN Document Server

We show that if $X$ is an infinite-dimensional separable Banach space (or more generally a Banach space with an infinite-dimensional separable quotient) then there is a continuous mapping $f\\colon X\\to X$ such that the autonomous differential equation $x'=f(x)$ has no solution at any point.

Hjek, Petr

2009-01-01

46

On universal Banach spaces of density continuum  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We consider the question whether there exists a Banach space $X$ of density continuum such that every Banach space of density not bigger than continuum isomorphically embeds into $X$ (called a universal Banach space of density $\\cc$). It is well known that $\\ell_\\infty/c_0$ is such a space if we assume the continuum hypothesis. However, some additional set-theoretic assumption is needed, as we prove in the main result of this paper that it is consistent with the usual axioms...

Brech, Christina; Koszmider, Piotr

2010-01-01

47

Incomparable, non isomorphic and minimal Banach spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

A Banach space contains either a minimal subspace or a continuum of incomparable subspaces. General structure results for analytic equivalence relations are applied in the context of Banach spaces to show that if $E_0$ does not reduce to isomorphism of the subspaces of a space, in particular, if the subspaces of the space admit a classification up to isomorphism by real numbers, then any subspace with an unconditional basis is isomorphic to its square and hyperplanes and has...

Rosendal, Christian

2004-01-01

48

Cross-frames in Banach spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

This paper generalizes results for alternate dual frames in Hilbert spaces on the situation of a Banach space. Additionally some properties of synthesys operator associated with alternate dual frame are investigated. The main result is that for a given cross-frame in Banach space we can not find such strongly continuous uniformely bounded one-parameter group of operators that the vectors from this cross-frame are eigenvectors of group's operators.

Kreys, Sergey

2011-01-01

49

The Banach space mp(X), for 1 ? p <8 has the Banach-Saks Property  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Problem statement: In the theory of Banach spaces one of the problems which describes geometric property of Banach spaces is Banach-Saks Property. In this context we were known many Banach spaces which had this property such as Lp[0, 1] for 1 Approach: Following the sequential structure of the Banach sequence space mp(X), for 1 ? p Results:

Braha, Naim L.

2009-01-01

50

M-ideals in Banach spaces and Banach algebras  

CERN Document Server

This book provides a comprehensive exposition of M-ideal theory, a branch ofgeometric functional analysis which deals with certain subspaces of Banach spaces arising naturally in many contexts. Starting from the basic definitions the authors discuss a number of examples of M-ideals (e.g. the closed two-sided ideals of C*-algebras) and develop their general theory. Besides, applications to problems from a variety of areas including approximation theory, harmonic analysis, C*-algebra theory and Banach space geometry are presented. The book is mainly intended as a reference volume for researchers working in one of these fields, but it also addresses students at the graduate or postgraduate level. Each of its six chapters is accompanied by a Notes-and-Remarks section which explores further ramifications of the subject and gives detailed references to the literature. An extensive bibliography is included.

Harmand, Peter; Werner, Wend

1993-01-01

51

On complete convergence in a Banach space  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Sufficient conditions are given under which a sequence of independent random elements taking values in a Banach space satisfy the Hsu and Robbins law of large numbers. The complete convergence of random indexed sums of random elements is also considered.

Anna Kuczmaszewska; Dominik Szynal

1994-01-01

52

VARIOUS SPACES FOR BANACH SPACE VALUED POTENTIAL HANKEL TRANSFORM  

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Full Text Available Different testing function spaces are defined for Banach space valued Potential Hankel transform by using Gelfand-Shilov technique of S? spaces, some properties of the spaces are also proved. At the end generalized Banach space valued Potential Hankel transform is defined.

NANDA D. SAHU

2011-12-01

53

Interpolation of quasi-Banach spaces  

International Nuclear Information System (INIS)

This dissertation presents a method of complex interpolation for familities of quasi-Banach spaces. This method generalizes the theory for families of Banach spaces, introduced by others. Intermediate spaces in several particular cases are characterized using different approaches. The situation when all the spaces have finite dimensions is studied first. The second chapter contains the definitions and main properties of the new interpolation spaces, and an example concerning the Schatten ideals associated with a separable Hilbert space. The case of L/sup P/ spaces follows from the maximal operator theory contained in Chapter III. Also introduced is a different method of interpolation for quasi-Banach lattices of functions, and conditions are given to guarantee that the two techniques yield the same result. Finally, the last chapter contains a different, and more direct, approach to the case of Hardy spaces

1986-01-01

54

2-Cone Banach spaces and fixed point theorem  

Science.gov (United States)

The present article deals with 2-cone normed spaces, 2-cone Banach spaces. Also, some results expressing under what conditions a self-mapping T of 2-cone Banach space (X, ||.,.||c) has a unique fixed point are given.

Sahiner, Ahmet; Yigit, Tuba

2012-09-01

55

Fixed Points of Expansive Type Mappings in 2-Banach Spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

In present paper, we define expansive mappings in 2-Banach space and prove some common unique fixed point theorems which are the extension of results of Wang et al. [12] and Rhoades [9] in 2-Banach space.

2013-01-01

56

On Sharp Triangle Inequalities in Banach Spaces II  

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Full Text Available Sharp triangle inequality and its reverse in Banach spaces were recently showed by Mitani et al. (2007. In this paper, we present equality attainedness for these inequalities in strictly convex Banach spaces.

Saito Kichi-Suke

2010-01-01

57

On Sharp Triangle Inequalities in Banach Spaces II  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Sharp triangle inequality and its reverse in Banach spaces were recently showed by Mitani et al. (2007). In this paper, we present equality attainedness for these inequalities in strictly convex Banach spaces.

Ken-Ichi Mitani; Kichi-Suke Saito

2010-01-01

58

Fixed Points of Expansive Type Mappings in 2-Banach Spaces  

Directory of Open Access Journals (Sweden)

Full Text Available In present paper, we define expansive mappings in 2-Banach space and prove some common unique fixed point theorems which are the extension of results of Wang et al. [12] and Rhoades [9] in 2-Banach space.

Prabha Chouhan

2013-08-01

59

A class of Banach spaces with few non strictly singular operators  

CERN Document Server

We construct a family $(\\mathcal{X}_\\al)_{\\al\\le \\omega_1}$ of reflexive Banach spaces with long transfinite bases but with no unconditional basic sequences. In our spaces $\\mathcal{X}_\\al$ every bounded operator $T$ is split into its diagonal part $D_T$ and its strictly singular part $S_T$.

Argyros, S A; Todorcevic, S

2003-01-01

60

Embedding into Banach spaces with finite dimensional decompositions  

Digital Repository Infrastructure Vision for European Research (DRIVER)

This paper deals with the following types of problems: Assume a Banach space $X$ has some property (P). Can it be embedded into some Banach space $Z$ with a finite dimensional decomposition having property (P), or more generally, having a property related to (P)? Secondly, given a class of Banach spaces, does there exist a Banach space in this class, or in a closely related one, which is universal for this class?

Odell, E.; Schlumprecht, Th

2007-01-01

 
 
 
 
61

Implicit Functions from Topological Vector Spaces to Banach Spaces  

CERN Multimedia

We prove implicit function theorems for mappings on topological vector spaces over valued fields. In the real and complex cases, we obtain implicit function theorems for mappings from arbitrary (not necessarily locally convex) topological vector spaces to Banach spaces.

Glockner, H

2003-01-01

62

Fixed Point Theorems in Cone Banach Spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

In this manuscript, a class of self-mappings on cone Banach spaces which have at least one fixed point is considered. More precisely, for a closed and convex subset C of a cone Banach space with the norm ?x?P=d(x,0), if there exist a, b, s and T:C?C satisfies the conditions 0?s+|a|?2b<2(a+b) and 4ad(Tx,Ty)+b(d(x,Tx)+d(y,Ty))?sd(x,y) for all x,y?C , then T has at least one Fixed point.

Nar, Erdal Karap X.

2009-01-01

63

Isomorphic Schauder decompositions in certain Banach spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We extend a theorem of Kato on similarity for sequences of projections in Hilbert spaces to the case of isomorphic Schauder decompositions in certain Banach spaces. To this end we use $\\ell_{\\Psi}$-Hilbertian and $\\infty$-Hilbertian Schauder decompositions instead of orthogonal Schauder decompositions, generalize the concept of an orthogonal Schauder decomposition in a Hilbert space and introduce the class of spaces with Schauder-Orlicz decompositions. Furthermore, we genera...

Marchenko, Vitalii

2013-01-01

64

Even infinite dimensional real Banach spaces  

CERN Document Server

This article is a continuation of a paper of the first author \\cite{F} about complex structures on real Banach spaces. We define a notion of even infinite dimensional real Banach space, and prove that there exist even spaces, including HI or unconditional examples from \\cite{F} and $C(K)$ examples due to Plebanek \\cite{P}. We extend results of \\cite{F} relating the set of complex structures up to isomorphism on a real space to a group associated to inessential operators on that space, and give characterizations of even spaces in terms of this group. We also generalize results of \\cite{F} about totally incomparable complex structures to essentially incomparable complex structures, while showing that the complex version of a space defined by S. Argyros and A. Manoussakis \\cite{AM} provide examples of essentially incomparable complex structures which are not totally incomparable.

Ferenczi, Valentin

2007-01-01

65

Invariant manifolds for flows in Banach Spaces  

Energy Technology Data Exchange (ETDEWEB)

The author considers the existence, smoothness and exponential attractivity of global invariant manifolds for flow in Banach Spaces. He shows that every global invariant manifold can be expressed as a graph of a C{sup k} map, provided that the invariant manifolds are exponentially attractive. Applications go to the Reaction-Diffusion equation, the Kuramoto-Sivashinsky equation, and singular perturbed wave equation.

Lu Kening.

1989-01-01

66

Remarks on quadratic equations in Banach space  

Directory of Open Access Journals (Sweden)

Full Text Available We find new sufficient conditions for the uniqueness of solutions of quadratic and in general multilinear equations in a Banach space X, by assuming the existence of a certain limit of linear operators in a suitable subspace of X.

Ioannis K. Argyros

1990-09-01

67

A characterization of banach spaces containing L.  

Science.gov (United States)

It is proved that a Banach space contains a subspace isomorphic to l(1) if (and only if) it has a bounded sequence with no weak-Cauchy subsequence. The proof yields that a sequence of subsets of a given set has a subsequence that is either convergent or Boolean independent. PMID:16592162

Rosenthal, H P

1974-06-01

68

A Hilbert space structure on Banach algebras  

International Nuclear Information System (INIS)

In this note we define an inner product on ''reduced'' Banach *-algebras via a measure on the set of positive functionals. It is shown here that the resultant inner product space is a topological algebra and also a completeness condition is obtained. (author). 9 refs

1988-01-01

69

Discretization of variational regularization in Banach spaces  

CERN Document Server

Consider a nonlinear ill-posed operator equation $F(u)=y$ where $F$ is defined on a Banach space $X$. In general, for solving this equation numerically, a finite dimensional approximation of $X$ and an approximation of $F$ are required. Moreover, in general the given data $\\yd$ of $y$ are noisy. In this paper we analyze finite dimensional variational regularization, which takes into account operator approximations and noisy data: We show (semi-)convergence of the regularized solution of the finite dimensional problems and establish convergence rates in terms of Bregman distances under appropriate sourcewise representation of a solution of the equation. The more involved case of regularization in nonseparable Banach spaces is discussed in detail. In particular we consider the space of finite total variation functions, the space of functions of finite bounded deformation, and the $L^\\infty$--space.

Poeschl, C; Scherzer, O

2010-01-01

70

Banach spaces of vector-valued functions  

CERN Document Server

"When do the Lebesgue-Bochner function spaces contain a copy or a complemented copy of any of the classical sequence spaces?" This problem and the analogous one for vector- valued continuous function spaces have attracted quite a lot of research activity in the last twenty-five years. The aim of this monograph is to give a detailed exposition of the answers to these questions, providing a unified and self-contained treatment. It presents a great number of results, methods and techniques, which are useful for any researcher in Banach spaces and, in general, in Functional Analysis. This book is written at a graduate student level, assuming the basics in Banach space theory.

Cembranos, Pilar

1997-01-01

71

Three-space problems in Banach space theory  

CERN Document Server

This book on Banach space theory focuses on what have been called three-space problems. It contains a fairly complete description of ideas, methods, results and counterexamples. It can be considered self-contained, beyond a course in functional analysis and some familiarity with modern Banach space methods. It will be of interest to researchers for its methods and open problems, and to students for the exposition of techniques and examples.

Castillo, Jess M F

1997-01-01

72

Factorizations of EP Banach space operators and EP Banach algebra elements  

Digital Repository Infrastructure Vision for European Research (DRIVER)

EP Banach space operators and EP Banach algebra elements are characterized using different kinds of factorizations. The results obtained generalize well-known characterizations of EP matrices, EP Hilbert space operators and EP $C^*$-algebra elements. Furthermore, new results that hold in these contexts are presented.

Boasso, Enrico

2013-01-01

73

Characterizations of EP and normal Banach algebra elements and Banach space operators  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Several characterizations of EP and normal Moore-Penrose invertible Banach algebra elements will be considered. The Banach space operator case will be also studied. The results of the present article will extend well known facts obtained in the frames of matrices and Hilbert space operators.

Boasso, Enrico; Rakoc?evic?, Vladimir

2013-01-01

74

Submonotone mappings in Banach spaces and applications  

International Nuclear Information System (INIS)

The notions 'submonotone' and 'strictly submonotone' mapping, introduced by J. Spingarn in Rn, are extended in a natural way to arbitrary Banach spaces. Several results about monotone operators are proved for submonotone and strictly submonotone ones: Rockafellar's result about local boundedness of monotone operators; Kenderov's result about single-valuedness and upper-semicontinuity almost everywhere of monotone operators in Asplund spaces; minimality (as w* - cusco mappings) of maximal strictly submonotone mappings, etc. It is shown that subdifferentials of various classes non-convex functions defined as pointwise suprema of quasi-differentiable functions possess submonotone properties. Results about generic differentiability of such functions are obtained (among them are new generalizations of an Ekeland and Lebourg's theorem). Applications are given to the properties of the distance function in a Banach space with uniformly Gateaux differentiable norm. (author). 29 refs

1995-01-01

75

Iterative schemes for computing fixed points of nonexpansive mappings in Banach spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Let $X$ be a real Banach space with a normalized duality mapping uniformly norm-to-weak$^\\star$ continuous on bounded sets or a reflexive Banach space which admits a weakly continuous duality mapping $J_{\\Phi}$ with gauge $\\phi$. Let $f$ be an {\\em $\\alpha$-contraction} and $\\{T_n\\}$ a sequence of nonexpansive mapping, we study the strong convergence of explicit iterative schemes x_{n+1} = \\alpha_n f(x_n) + (1-\\alpha_n) T_n x_n with a general theorem and then recover ...

Chancelier, Jean-philippe

2007-01-01

76

Spreading Models in Banach Space Theory  

CERN Document Server

We extend the classical Brunel-Sucheston definition of the spreading model by introducing the $\\mathcal{F}$-sequences $(x_s)_{s\\in\\mathcal{F}}$ in a Banach space and the plegma families in $\\mathcal{F}$ where $\\mathcal{F}$ is a regular thin family. The new concept yields a transfinite increasing hierarchy of classes of 1-subsymmetric sequences. We explore the corresponding theory and we present examples establishing this hierarchy and illustrating the limitation of the theory.

Argyros, S A; Tyros, K

2010-01-01

77

Polynomials and identities on real Banach spaces.  

Czech Academy of Sciences Publication Activity Database

. Ro?. 385, ?. 2 (2012), s. 1015-1026. ISSN 0022-247XGrant CEP: GA ?R(CZ) GAP201/11/0345Vzkumn zm?r: CEZ:AV0Z10190503Kl?ov slova: Polynomials on Banach spacesKd oboru RIV: BA - Obecn matematikaImpakt faktor: 1.050, rok: 2012http://www.sciencedirect.com/science/article/pii/S0022247X11006743

Hjek, Petr Pavel; Kraus, M.

78

Complemented subspaces of p-adic second dual Banach spaces  

Directory of Open Access Journals (Sweden)

Full Text Available Let K be a non-archimedean non-trivially valued complete field. In this paper we study Banach spaces over K. Some of main results are as follows: (1 The Banach space BC((l∞1 has an orthocomplemented subspace linearly homeomorphic to c0. (2 The Banach space BC((c01 has an orthocomplemented subspace linearly homeomorphic to l∞.

Takemitsu Kiyosawa

1995-09-01

79

Metrizability of Cone Metric Spaces Via Renorming the Banach Spaces  

CERN Document Server

In this paper we show that by renorming an ordered Banach space, every cone P can be converted to a normal cone with constant K = 1 and consequently due to this approach every cone metric space is really a metric one and every theorem in metric space valid for cone metric space automatically.

Asadi, Mehdi; Soleiman, Hossein

2011-01-01

80

Metrizability of Cone Metric Spaces Via Renorming the Banach Spaces  

Directory of Open Access Journals (Sweden)

Full Text Available In this paper we show that by renorming an ordered Banach space, every cone $P$ can be converted to a normal cone with constant $K=1$ and consequently due to this approach every cone metric space is really a metric one and every theorem in metric space is valid for cone metric space automatically.

Hossein Soleimani

2012-09-01

 
 
 
 
81

On quotients of Banach spaces having shrinking unconditional bases  

Digital Repository Infrastructure Vision for European Research (DRIVER)

It is proved that if a Banach space $Y$ is a quotient of a Banach space having a shrinking unconditional basis, then every normalized weakly null sequence in $Y$ has an unconditional subsequence. The proof yields the corollary that every quotient of Schreier's space is $c_o$-saturated.

Odell, Edward

1990-01-01

82

Introduction to Banach spaces and algebras  

CERN Multimedia

Banach spaces and algebras are a key topic of pure mathematics. Graham Allan's careful and detailed introductory account will prove essential reading for anyone wishing to specialise in functional analysis and is aimed at final year undergraduates or masters level students. Based on the author's lectures to fourth year students at Cambridge University, the book assumes knowledge typical of first degrees in mathematics, including metric spaces, analytic topology, and complexanalysis. However, readers are not expected to be familiar with the Lebesgue theory of measure and integration.The text be

Allan, Graham

2010-01-01

83

Discretization of variational regularization in Banach spaces  

International Nuclear Information System (INIS)

Consider a nonlinear ill-posed operator equation F(u) = y, where F is defined on a Banach space X. In this paper we analyze finite-dimensional variational regularization, which takes into account operator approximations and noisy data. As shown in the literature, depending on the setting, convergence of the regularized solutions of the finite-dimensional problems can be with respect to the strong or just a weak topology. In this paper our contribution is twofold. First, we derive convergence rates in terms of Bregman distances in the convex regularization setting under appropriate sourcewise representation of a solution of the equation. Secondly, for particular regularization realizations in nonseparable Banach spaces, we discuss the finite-dimensional approximations of the spaces and the type of convergence, which is needed for the convergence analysis. These considerations lay the fundament for efficient numerical implementation. In particular, we emphasize on the space X of finite total variation functions and analyze in detail the cases when X is the space of the functions of finite bounded deformation and the L?-space. The latter two settings are of interest in numerous problems arising in optimal control, machine learning and engineering

2010-10-01

84

Characterizations of metric projections in Banach spaces and applications  

Directory of Open Access Journals (Sweden)

Full Text Available This paper is devoted to the study of the metric projection onto a nonempty closed convex subset of a general Banach space. Thanks to a systematic use of semi-inner products and duality mappings, characterizations of the metric projection are given. Applications to decompositions of Banach spaces along convex cones and variational inequalities are presented.

Jean-Paul Penot

1998-01-01

85

Infinite order decoupling of random chaoses in Banach space  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We prove a number of decoupling inequalities for nonhomogeneous random polynomials with coefficients in Banach space. Degrees of homogeneous components enter into comparison as exponents of multipliers of terms of certain Poincar\\'e-type polynomials. It turns out that the fulfillment of most of types of decoupling inequalities may depend on the geometry of Banach space.

Szulga, Jerzy

1992-01-01

86

Impulsive integral equations in Banach spaces and applications  

Directory of Open Access Journals (Sweden)

Full Text Available In this paper, we first use the fixed point theory to prove two existence theorems of positive solutions for the impulsive Fredholm integral Equations in Banach spaces. And then, we offer some applications to the two-point boundary value problems for the second order impulsive differential equations in Banach spaces.

Dajun Guo

1992-01-01

87

Nonlinear impulsive Volterra integral equations in Banach spaces and applications  

Digital Repository Infrastructure Vision for European Research (DRIVER)

In this paper, we first extend results on the existence of maximal solutions for nonlinear Volterra integral equations in Banach spaces to impulsive Volterra integral equations. Then, we give some applications to initial value problems for first order impulsive differential equations in Banach spaces. The results are demonstrated by means of an example of an infinite system for impulsive differential equations.

1993-01-01

88

Impulsive integral equations in Banach spaces and applications  

Digital Repository Infrastructure Vision for European Research (DRIVER)

In this paper, we first use the fixed point theory to prove two existence theorems of positive solutions for the impulsive Fredholm integral Equations in Banach spaces. And then, we offer some applications to the two-point boundary value problems for the second order impulsive differential equations in Banach spaces.

1992-01-01

89

Nonlinear impulsive Volterra integral equations in Banach spaces and applications  

Directory of Open Access Journals (Sweden)

Full Text Available In this paper, we first extend results on the existence of maximal solutions for nonlinear Volterra integral equations in Banach spaces to impulsive Volterra integral equations. Then, we give some applications to initial value problems for first order impulsive differential equations in Banach spaces. The results are demonstrated by means of an example of an infinite system for impulsive differential equations.

Dajun Guo

1993-01-01

90

The strong WCD property for Banach spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

In this paper, we introduce weakly compact version of the weakly countably determined (WCD) property, the strong WCD (SWCD) property. A Banach space X is said to be SWCD if there s a sequence (An) of weak ∗ compact subsets of X∗∗ such that if K⊂X is weakly compact, there is an (nm)⊂N such that K⊂⋂m=1∞Anm⊂X. In this case, (An) is called a strongly determining sequence for X. We show that...

1995-01-01

91

Banach spaces adapted to Anosov systems  

CERN Multimedia

We study the spectral properties of the Ruelle-Perron-Frobenius operator associated to an Anosov map on classes of functions with high smoothness. To this end we construct anisotropic Banach spaces of distributions on which the transfer operator has a large spectral gap. In the C^\\infty case, the spectral radius is arbitrarily small, which yields a description of the correlations with arbitrary precision. Moreover, we obtain sharp spectral stability results for deterministic and random perturbations. In particular, we obtain differentiability results for spectral data (which imply differentiability of the SRB measure, the variance for the CLT, the rates of decay for smooth observable, etc.).

Gouezel, S; Gouezel, Sebastien; Liverani, Carlangelo

2004-01-01

92

Some results concerning frames in Banach spaces  

Directory of Open Access Journals (Sweden)

Full Text Available A necessary and sufficient condition for the associated sequence of functionals to a complete minimal sequence to be a Banach frame has been given. We give the definition of a weak-exact Banach frame, and observe that an exact Banach frame is weak-exact. An example of a weak-exact Banach frame which is not exact has been given. A necessary and sufficient condition for a Banach frame to be a weak-exact Banach frame has been obtained. Finally, a necessary condition for the perturbation of a retro Banach frame by a finite number of linearly independent vectors to be a retro Banach frame has been given.

S. K. Kaushik

2007-09-01

93

An Implicit Iterative Scheme for an Infinite Countable Family of Asymptotically Nonexpansive Mappings in Banach Spaces  

Directory of Open Access Journals (Sweden)

Full Text Available Abstract Let be a nonempty closed convex subset of a reflexive Banach space with a weakly continuous dual mapping, and let be an infinite countable family of asymptotically nonexpansive mappings with the sequence satisfying for each , , and for each . In this paper, we introduce a new implicit iterative scheme generated by and prove that the scheme converges strongly to a common fixed point of , which solves some certain variational inequality.

Wang Shenghua

2008-01-01

94

A Strong Convergence Theorem for a Family of Quasi-?-Nonexpansive Mappings in a Banach Space  

Directory of Open Access Journals (Sweden)

Full Text Available The purpose of this paper is to propose a modified hybrid projection algorithm and prove a strong convergence theorem for a family of quasi-?-nonexpansive mappings. The strong convergence theorem is proven in the more general reflexive, strictly convex, and smooth Banach spaces with the property (K. The results of this paper improve and extend the results of S. Matsushita and W. Takahashi (2005, X. L. Qin and Y. F. Su (2007, and others.

Haiyun Zhou

2009-01-01

95

A Strong Convergence Theorem for a Family of Quasi- -Nonexpansive Mappings in a Banach Space  

Directory of Open Access Journals (Sweden)

Full Text Available The purpose of this paper is to propose a modified hybrid projection algorithm and prove a strong convergence theorem for a family of quasi- -nonexpansive mappings. The strong convergence theorem is proven in the more general reflexive, strictly convex, and smooth Banach spaces with the property (K. The results of this paper improve and extend the results of S. Matsushita and W. Takahashi (2005, X. L. Qin and Y. F. Su (2007, and others.

Gao Xinghui

2009-01-01

96

Renorming Banach spaces with the Mazur intersection property  

Digital Repository Infrastructure Vision for European Research (DRIVER)

In this paper we give new sufficient and necessary conditions for a Banach space to be equivalently renormed with the Mazur intersection property. As a consequence, several examples and applications of these results are obtained. Among them, it is proved that every Banach space embeds isometrically into a Banach space with the Mazur intersection property, answering a question asked by Giles, Gregory, and Sims. We also prove that for every treeT, the spaceC0(T) admits a norm with the Mazur int...

1997-01-01

97

Iterative Approximation of a Common Zero of a Countably Infinite Family of -Accretive Operators in Banach Spaces  

Directory of Open Access Journals (Sweden)

Full Text Available Abstract Let be a real reflexive and strictly convex Banach space which has a uniformly Gteaux differentiable norm and be a closed convex nonempty subset of . Strong convergence theorems for approximation of a common zero of a countably infinite family of -accretive mappings from to are proved. Consequently, we obtained strong convergence theorems for a countably infinite family of pseudocontractive mappings.

Ofoedu EU

2008-01-01

98

Generalized dissipativeness in a Banach space  

Directory of Open Access Journals (Sweden)

Full Text Available Suppose X is a real or complex Banach space with dual X* and a semiscalar product [,]. For k a real number, a subset B of X×X will be called k-dissipative if for each pair of elements (x1,y1, (x2,y2 in B, there existsh∈{f∈X*:[x,f]=|x|2=|f|2}such thatRe[y1−y2,h]≤k|x1−x2|2.This definition extends a notion of dissipativeness which is equivalent to having k equal zero here. A number of definitions and theorems related to this original dissipative notion are generalized in the present paper to fit the k-dissipative situation, and proofs are given for the new theorems.

David R. Gurney

1996-03-01

99

Banach spaces of functions analytic in a polydisc  

Directory of Open Access Journals (Sweden)

Full Text Available This paper is concerned with functions of several complex variables analytic in the unit polydisc. Certain Banach spaces to which these functions might belong are defined and some relationships between them are developed. The space of linear functionals for the Banach space of functions analytic in the open unit polydisc and continuous on the unit torus is then described in terms of analytic functions using an extension of the Hadamard product.

Leon M. Hall

1986-03-01

100

Nigel Kalton's work in isometrical Banach space theory  

CERN Multimedia

This paper surveys some of the late Nigel Kalton's contributions to Banach space theory. The paper is written for the Nigel Kalton Memorial Website http://mathematics.missouri.edu/kalton/, which is scheduled to go online in summer 2011.

Werner, Dirk

2011-01-01

 
 
 
 
101

Diophantine approximations and convergence of series in Banach spaces  

Directory of Open Access Journals (Sweden)

Full Text Available n this paper we give a new proof of a known diophantine approximation result, then we apply this to prove convergence of a class of series in a Banach space, whose terms are defined recursively.

Giovanni Fiorito

1993-11-01

102

On $ R $-subcommuting maps and best approximations in Banach spaces  

Directory of Open Access Journals (Sweden)

Full Text Available A result on best approximation is proved in Banach spaces satisfying Opial's condition. Recent results of Jungck and Sessa [Math. Japonica, 42(1995, 249-252.] are extended to a new class of noncommuting maps.

Naseer Shahzad

2001-03-01

103

On second order impulsive functional differential equations in Banach spaces  

Directory of Open Access Journals (Sweden)

Full Text Available In this paper, a fixed point theorem due to Schaefer is used to investigate the existence of solutions for second order impulsive functional differential equations in Banach spaces.

M. Benchohra

2002-01-01

104

Some Modulus and Normal Structure in Banach Space  

Directory of Open Access Journals (Sweden)

Full Text Available We present some sufficient conditions for which a Banach space X has normal structure in terms of the modulus of U-convexity, modulus of W?-convexity, and the coefficient R(1,X, which generalized some well-known results. Furthermore the relationship between modulus of convexity, modulus of smoothness, and Gao's constant is considered, meanwhile the exact value of Milman modulus has been obtained for some Banach space.

Zhanfei Zuo

2009-01-01

105

Some Modulus and Normal Structure in Banach Space  

Directory of Open Access Journals (Sweden)

Full Text Available Abstract We present some sufficient conditions for which a Banach space has normal structure in terms of the modulus of -convexity, modulus of -convexity, and the coefficient , which generalized some well-known results. Furthermore the relationship between modulus of convexity, modulus of smoothness, and Gao's constant is considered, meanwhile the exact value of Milman modulus has been obtained for some Banach space.

Zuo Zhanfei

2009-01-01

106

Asymptotically convex Banach spaces and The Index of Rotundity Problem  

Scientific Electronic Library Online (English)

Full Text Available SciELO Chile | Language: English Abstract in english The Index of Rotundity Problem asks whether a Banach space which admits equivalent renormings with index of rotundity as small as desired also admits an equivalent rotund renorming. In this paper we continue the ongoing search for a negative answer to this question by making use of a new concept: as [...] ymptotically convex Banach spaces. Some applications to The Approximation Hyperplane Series Property are given.

Francisco J, Garca-Pacheco.

107

Asymptotically convex Banach spaces and The Index of Rotundity Problem  

Directory of Open Access Journals (Sweden)

Full Text Available The Index of Rotundity Problem asks whether a Banach space which admits equivalent renormings with index of rotundity as small as desired also admits an equivalent rotund renorming. In this paper we continue the ongoing search for a negative answer to this question by making use of a new concept: asymptotically convex Banach spaces. Some applications to The Approximation Hyperplane Series Property are given.

Francisco J Garca-Pacheco

2012-06-01

108

Embeddings of Banach Spaces into Banach Lattices and the Gordon-Lewis Property  

Digital Repository Infrastructure Vision for European Research (DRIVER)

In this paper we first show that if $X$ is a Banach space and $\\alpha$ is a left invariant crossnorm on $\\ell_\\infty\\otimes X$, then there is a Banach lattice $L$ and an isometric embedding $J$ of $X$ into $L$, so that $I\\otimes J$ becomes an isometry of $\\ell_\\infty\\otimes_\\alpha X$ onto $\\ell_\\infty\\otimes_m J(X)$. Here $I$ denotes the identity operator on $\\ell_\\infty$ and $\\ell_\\infty\\otimes_m J(X)$ the canonical lattice tensor product. This result is originally due to G...

Casazza, Peter G.; Nielsen, N. J.

1998-01-01

109

Integral operators on the section space of a Banach bundle  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Let π:E→X and ρ:F→X be bundles of Banach spaces, where X is a compact Hausdorff space, and let V be a Banach space. Let Γ(π) denote the space of sections of the bundle π. We obtain two representations of integral operators T:Γ(π)→V in terms of measures. The first generalizes a recent result of P. Saab, the second generalizes a theorem of Grothendieck. We also study integral op...

Kitchen, J. W.; Robbins, D. A.

1993-01-01

110

Banach's space: Lviv and the Scottish cafe  

Directory of Open Access Journals (Sweden)

Full Text Available In a sense Stefan Banach is the patron saint of this workshop. He was one of the most prominent former residents of Lviv. His ``hangout'', the Scottish Cafe, is shown in the street scene that is the cover of the book of abstracts.

D.Henderson

2004-01-01

111

Convergence on Composite Iterative Schemes for Nonexpansive Mappings in Banach Spaces  

Directory of Open Access Journals (Sweden)

Full Text Available Abstract Let be a reflexive Banach space with a uniformly Gteaux differentiable norm. Suppose that every weakly compact convex subset of has the fixed point property for nonexpansive mappings. Let be a nonempty closed convex subset of , a contractive mapping (or a weakly contractive mapping, and nonexpansive mapping with the fixed point set . Let be generated by a new composite iterative scheme: , , . It is proved that converges strongly to a point in , which is a solution of certain variational inequality provided that the sequence satisfies and , for some and the sequence is asymptotically regular.

Jung JongSoo

2008-01-01

112

Proper metrics on locally compact groups, and proper affine isometric actions on Banach spaces  

CERN Multimedia

In this article it is proved, that every locally compact second countable group has a left invariant metric d, which generates the topology on G, and which is proper, ie. every closed d-bounded set in G is compact. Moreover, we obtain the following extension of a result due to N. Brown and E. Guentner: Every locally compact second countable $G$ admits a proper affine action on the reflexive and strictly convex Banach space $\\bigoplus^{\\infty}_{n=1} L^{2n}(G, d\\mu),$ where the direct sum is taken in the $l^2$-sense.

Haagerup, U; Haagerup, Uffe; Przybyszewska, Agata

2006-01-01

113

Convergence on Composite Iterative Schemes for Nonexpansive Mappings in Banach Spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Let E be a reflexive Banach space with a uniformly Gâteaux differentiable norm. Suppose that every weakly compact convex subset of E has the fixed point property for nonexpansive mappings. Let C be a nonempty closed convex subset of E, f:C  →  C a contractive mapping (or a weakly contractive mapping), and T:C  →  C nonexpansive mapping with the fixed point s...

Jong Soo Jung

2008-01-01

114

Games in Banach spaces: Questions and several answers  

CERN Multimedia

Aronszajn-null sets are a notion of negligible sets for infinite dimensional Banach spaces generalizing Lebesgue measure zero sets on the real line and the Euclidean space. We present a game-theoretic approach to Aronszajn null sets, and discuss the ensuing open problems.

Duda, J; Duda, Jakub; Tsaban, Boaz

2006-01-01

115

Spectral synthesis and topologies on ideal spaces for Banach *-algebras  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Abstract This paper continues the study of spectral synthesis and the topologies Tau-infinity and Tau-r on the ideal space of a Banach algebra, concentrating on the class of Banach *-algebras, and in particular on L 1 -group algebras. It is shown that if a group G is a infnite extension of an abelian group then Tau-r is Hausdorff on the ideal space of L 1 (G) if and only if L 1 (G) has spectral synthesis, which in turn is equivalent to G being compact. The result is applied to ...

Feinstein, J. F.; Kaniuth, E.

1999-01-01

116

Structure of total subspaces of dual Banach spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Let $X$ be a separable nonquasireflexive Banach space. Let $Y$ be a Banach space isomorphic to a subspace of $X^*$. The paper is devoted to the following questions: 1. Under what conditions does there exist an isomorphic embedding $T:Y\\to X^*$ such that subspace $T(Y)\\subset X^*$ is total? 2. If such embeddings exist, what are the possible orders of $T(Y)$? Here we need to recall some definitions. For a subset $M\\subset X^*$ we denote the set of all limits of weak$^*$ conv...

Ostrovskii, Mikhail I.

1993-01-01

117

Banach spaces and descriptive set theory selected topics  

CERN Multimedia

This volume deals with problems in the structure theory of separable infinite-dimensional Banach spaces, with a central focus on universality problems. This topic goes back to the beginnings of the field and appears in Banach's classical monograph. The novelty of the approach lies in the fact that the answers to a number of basic questions are based on techniques from Descriptive Set Theory. Although the book is oriented on proofs of several structural theorems, in the main text readers will also find a detailed exposition of numerous intermediate results which are interesting in their own right and have proven to be useful in other areas of Functional Analysis. Moreover, several well-known results in the geometry of Banach spaces are presented from a modern perspective.

Dodos, Pandelis

2010-01-01

118

Coincidence and fixed point theorems in metric and Banach spaces  

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Full Text Available We prove some coincidence and fixed point theorems for generalized (ϕ,f-contractive type and f-nonexpansive type multivalued and singlevalued mappings in metric and Banach spaces, respectively. Our results extend, improve, and unify a few known results due to Browder, Browder and Petryshyn, Chang, Huang, and Cho, Husain and Latif, Husain and Tarafdar, and Karlovitz.

Mohammad S. Khan

2001-05-01

119

The reconstruction property in Banach spaces and a perturbation theorem  

DEFF Research Database (Denmark)

Perturbation theory is a fundamental tool in Banach space theory. However, the applications of the classical results are limited by the fact that they force the perturbed sequence to be equivalent to the given sequence. We will develop a more general perturbation theory that does not force equivalence of the sequences.

Christensen, Ole

2008-01-01

120

Multivalued impulsive neutral functional differential inclusions in Banach spaces  

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Full Text Available In paper the existence of solutions for first and second order impulsive neutral functional differential inclusions in Banach spaces is investigated. The results are obtained by using a fixed point theorem for condensing multivalued maps due to Martelli and the semigroup theory.

M. Benchohra

2002-03-01

 
 
 
 
121

On antichains of spreading models of Banach spaces  

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We show that for every separable Banach space $X$, either $\\spw(X)$ (the set of all spreading models of $X$ generated by weakly-null sequences in $X$, modulo equivalence) is countable, or $\\spw(X)$ contains an antichain of the size of the continuum. This answers a question of S. J. Dilworth, E. Odell and B. Sari.

Dodos, Pandelis

2008-01-01

122

Multipliers and Toeplitz operators on Banach spaces of sequences  

CERN Multimedia

We prove that every multiplier M (bounded operator commuting with the shift operator) on a large class of Banach spaces of sequences on Z is associated to a function essentially bounded by the norm of M on the spectrum of S.

Petkova, V

2006-01-01

123

Nonlocal fractional semilinear differential equations in separable Banach spaces  

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Full Text Available In this article, we study the existence of mild solutions for fractional semilinear differential equations with nonlocal conditions in separable Banach spaces. The result is obtained by using the Hausdorff measure of noncompactness and the Schauder fixed point theorem.

Kexue Li

2013-01-01

124

The Invariant Subspace Problem for Non-Archimedean Banach Spaces  

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It is proved that every infinite-dimensional non-archimedean Banach space of countable type admits a linear continuous operator without a non-trivial closed invariant subspace. This solves a problem stated by A. C. M. van Rooij and W. H. Schikhof in 1992.

S?liwa, Wies?aw

2008-01-01

125

On polynomial equations in Banach space, perturbation techniques and applications  

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Full Text Available We use perturbation techniques to solve the polynomial equation in Banach space. Our techniques provide more accurate information on the location of solutions and yield existence and uniqueness in cases not covered before. An example is given to justify our method.

Ioannis K. Argyros

1987-03-01

126

A quasimartingale characterization of p stable type Banach spaces  

CERN Document Server

We characterize Banach spaces B of stable type p (1 < p < 2) by the property that for every sequence (X_i) of B-valued random variables, independent, centered and fulfilling some integrability assumption, the sequence S_n/n^(1/p) is a quasimartingale, where S_n=X_1+...+X_n.

Hechner, Florian

2010-01-01

127

On some impulsive fractional differential equations in Banach spaces  

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Full Text Available This paper deals with some impulsive fractional differential equations in Banach spaces. Utilizing the Leray-Schauder fixed point theorem and the impulsive nonlinear singular version of the Gronwall inequality, the existence of PC-mild solutions for some fractional differential equations with impulses are obtained under some easily checked conditions. At last, an example is given for demonstration.

W. Wei

2010-01-01

128

Continuous local martingales and stochastic integration in UMD Banach spaces:  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Recently, van Neerven, Weis and the author, constructed a theory for stochastic integration of UMD Banach space valued processes. Here the authors use a (cylindrical) Brownian motion as an integrator. In this note we show how one can extend these results to the case where the integrator

Veraar, M. C.

2007-01-01

129

Moment bounds for dependent sequences in smooth Banach spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We prove a Marcinkiewicz-Zygmund type inequality for random variables taking values in a smooth Banach space. Next, we obtain some sharp concentration inequalities for the empirical measure of {T, T^2, ..., T^n}, on a class of smooth functions, when T belongs to a class of nonuniformly expanding maps of the unit interval.

2014-01-01

130

Topologies on the set of all subspaces of a banach space and related questions of banach space geometry  

Digital Repository Infrastructure Vision for European Research (DRIVER)

For a Banach space $X$ we shall denote the set of all closed subspaces of $X$ by $G(X)$. In some kinds of problems it turned out to be useful to endow $G(X)$ with a topology. The main purpose of the present paper is to survey results on two the most common topologies on $G(X)$.

Ostrovskii, Mikhail I.

1993-01-01

131

Functional differential equations with infinite delay in Banach spaces  

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Full Text Available In this paper, a definition of the fundamental operator for the linear autonomous functional differential equation with infinite delay in a Banach space is given, and some sufficient and necessary conditions of the fundamental operator being exponentially stable in abstract phase spaces which satisfy some suitable hypotheses are obtained. Moreover, we discuss the relation between the exponential asymptotic stability of the zero solution of nonlinear functional differential equation with infinite delay in a Banach space and the exponential stability of the solution semigroup of the corresponding linear equation, and find that the exponential stability problem of the zero solution for the nonlinear equation can be discussed only in the exponentially fading memory phase space.

Tijun Xiao

1991-09-01

132

Borsuk-Ulam theorem in infinite-dimensional Banach spaces  

International Nuclear Information System (INIS)

The well-known classical Borsuk-Ulam theorem has a broad range of applications to various problems. Its generalization to infinite-dimensional spaces runs across substantial difficulties because its statement is essentially finite-dimensional. A result established in the paper is a natural generalization of the Borsuk-Ulam theorem to infinite-dimensional Banach spaces. Applications of this theorem to various problems are discussed

2002-02-28

133

Quantum tomography with wavelet transform in Banach space on Homogeneous space  

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The intimate connection between the Banach space wavelet reconstruction method on homogeneous spaces with both singular and nonsingular vacuum vectors, and some of well known quantum tomographies, such as: Moyal-representation for a spin, discrete phase space tomography, tomography of a free particle, Homodyne tomography, phase space tomography and SU(1,1) tomography is explained. Also both the atomic decomposition and banach frame nature of these quantum tomographic example...

Jafarizadeh, M. A.; Mirzaee, M.; Rezaee, M.

2008-01-01

134

Strong convergence of an iterative sequence for maximal monotone operators in a Banach space  

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We first introduce a modified proximal point algorithm for maximal monotone operators in a Banach space. Next, we obtain a strong convergence theorem for resolvents of maximal monotone operators in a Banach space which generalizes the previous result by Kamimura and Takahashi in a Hilbert space. Using this result, we deal with the convex minimization problem and the variational inequality problem in a Banach space.

Fumiaki Kohsaka; Wataru Takahashi

2004-01-01

135

hdl.handle.net/11104/0228697"> Polynomial algebras and smooth functions in Banach spaces.  

Czech Academy of Sciences Publication Activity Database

al Analysis. Ro?. 266, ?. 3 (2014), s. 1627-1646. ISSN 0022-1236Grant CEP: GA ?R(CZ) GAP201/11/0345; GA Mk(CZ) 7AMB12FR003Institucionln podpora: RVO:67985840Kl?ov slova: polynomials in Banach spaceKd oboru RIV: BA - Obecn matematikaImpakt faktor: 1.252, rok: 2012http://www.sciencedirect.com/science/article/pii/S0022123613004588

D'Alessandro, Stefania; Hjek, Petr Pavel

136

Identification for a semilinear evolution equation in a Banach space  

International Nuclear Information System (INIS)

In this paper we prove an existence result for strict solutions to an identification problem for a first-order semilinear differential equation, in a general Banach space, subjected to an overdetermination expressed by means of a Lebesgue integral. Under the additional assumption that the C0-semigroup generated by the linear part has a sufficiently fast exponential decay, we prove the uniqueness and the continuous dependence of the solution on the data

2010-08-01

137

On nonautonomous second-order differential equations on Banach space  

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Full Text Available We show the existence and uniqueness of classical solutions of the nonautonomous second-order equation: u″(t=A(tu′(t+B(tu(t+f(t, 0≤t≤T; u(0=x0, u′(0=x1 on a Banach space by means of operator matrix method and apply to Volterra integrodifferential equations.

Nguyen Thanh Lan

2001-04-01

138

Parameter choice in Banach space regularization under variational inequalities  

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The authors study parameter choice strategies for Tikhonov regularization of nonlinear ill-posed problems in Banach spaces. The effectiveness of any parameter choice for obtaining convergence rates depend on the interplay of the solution smoothness and the nonlinearity structure, and it can be expressed concisely in terms of variational inequalities. Such inequalities are link conditions between the penalty term, the norm misfit and the corresponding error measure. The parameter choices unde...

2012-01-01

139

Identification for a semilinear evolution equation in a Banach space  

Science.gov (United States)

In this paper we prove an existence result for strict solutions to an identification problem for a first-order semilinear differential equation, in a general Banach space, subjected to an overdetermination expressed by means of a Lebesgue integral. Under the additional assumption that the C0-semigroup generated by the linear part has a sufficiently fast exponential decay, we prove the uniqueness and the continuous dependence of the solution on the data.

Lorenzi, Alfredo; Vrabie, Ioan I.

2010-08-01

140

Weak convergence of an iterative sequence for accretive operators in Banach spaces  

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Full Text Available Let be a nonempty closed convex subset of a smooth Banach space and let be an accretive operator of into . We first introduce the problem of finding a point such that where is the duality mapping of . Next we study a weak convergence theorem for accretive operators in Banach spaces. This theorem extends the result by Gol'shte?n and Tret'yakov in the Euclidean space to a Banach space. And using our theorem, we consider the problem of finding a fixed point of a strictly pseudocontractive mapping in a Banach space and so on.

Iiduka Hideaki

2006-01-01

 
 
 
 
141

On the generalized Roper-Suffridge extension operator in Banach spaces  

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The generalized Roper-Suffridge extension operator in Banach spaces is introduced. We prove that this operator preserves the starlikeness on some domains in Banach spaces and does not preserve convexity in some cases. Furthermore, the growth theorem and covering theorem of the corresponding mappings are given. Some results of Roper and Suffridge and Graham et al. in ℂn are extended to Banach spaces.

2005-01-01

142

Tools for Malliavin calculus in UMD Banach spaces  

CERN Multimedia

In this paper we study the Malliavin derivatives and Skorohod integrals for processes taking values in an infinite dimensional space. Such results are motivated by their applications to SPDEs and in particular financial mathematics. Vector-valued Malliavin theory in Banach space E is naturally restricted to spaces E which have the so-called UMD property, which arises in harmonic analysis and stochastic integration theory. We provide several new results and tools for the Malliavin derivatives and Skorohod integrals in an infinite dimensional setting. In particular, we prove weak characterizations, a chain rule for Lipschitz functions, a sufficient condition for pathwise continuity and an Ito formula for non-adapted processes.

Pronk, Matthijs

2012-01-01

143

Elements of mathematical theory of evolutionary equations in Banach spaces  

CERN Document Server

Evolutionary equations are studied in abstract Banach spaces and in spaces of bounded number sequences. For linear and nonlinear difference equations, which are defined on finite-dimensional and infinite-dimensional tori, the problem of reducibility is solved, in particular, in neighborhoods of their invariant sets, and the basics for a theory of invariant tori and bounded semi-invariant manifolds are established. Also considered are the questions on existence and approximate construction of periodic solutions for difference equations in infinite-dimensional spaces and the problem of extendibi

Samoilenko, Anatoly M

2013-01-01

144

A proximal point method for nonsmooth convex optimization problems in Banach spaces  

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Full Text Available In this paper we show the weak convergence and stability of the proximal point method when applied to the constrained convex optimization problem in uniformly convex and uniformly smooth Banach spaces. In addition, we establish a nonasymptotic estimate of convergence rate of the sequence of functional values for the unconstrained case. This estimate depends on a geometric characteristic of the dual Banach space, namely its modulus of convexity. We apply a new technique which includes Banach space geometry, estimates of duality mappings, nonstandard Lyapunov functionals and generalized projection operators in Banach spaces.

Y. I. Alber

1997-01-01

145

Weighted diffeomorphism groups of Banach spaces and weighted mapping groups  

CERN Multimedia

In this work, we construct and study certain classes of infinite dimensional Lie groups that are modelled on weighted function spaces. In particular, we construct a Lie group of weighted diffeomorphisms on a Banach space. Further, we also construct certain types of weighted mapping groups. Both the weighted diffeomorphism groups and the weighted mapping groups are shown to be regular Lie groups in Milnor's sense. We also discuss semidirect products of the former groups. Moreover, we study the integrability of Lie algebras of certain vector fields.

Walter, Boris

2010-01-01

146

Convergence theorems for Banach space valued integrable multifunctions  

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Full Text Available In this work we generalize a result of Kato on the pointwise behavior of a weakly convergent sequence in the Lebesgue-Bochner spaces LXP(Ω (1≤p≤∞. Then we use that result to prove Fatou's type lemmata and dominated convergence theorems for the Aumann integral of Banach space valued measurable multifunctions. Analogous convergence results are also proved for the sets of integrable selectors of those multifunctions. In the process of proving those convergence theorems we make some useful observations concerning the Kuratowski-Mosco convergence of sets.

Nikolaos S. Papageorgiou

1987-09-01

147

Spectral results for operators commuting with translations on Banach spaces of sequences on Zk and Z+  

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Full Text Available We study the spectrum of multipliers (bounded operators commuting with the shift operator on a Banach space of sequences on . Given a multiplier , we prove that where is the symbol of . We obtain a similar result for the spectrum of an operator commuting with the shift on a Banach space of sequences on . We generalize the results for multipliers on Banach spaces of sequences on .Estudiamos el espectro de los multiplicadores (operadores acotados que conmutan con el operador shift en un espacio de Banach de sucesiones en . Dado un multiplicador , probamos que donde es el smbolo de . Obtenemos un resultados similar para el espectro de un operador que conmuta con el shift en un espacio de Banach de sucesiones en . Generalizamos los resultados sobre multiplicadores en espacios de Banach de sucesiones en .

Violeta Petkova

2012-10-01

148

The Choquet-Deny equation in a Banach space  

CERN Document Server

Let $G$ be a locally compact group and $\\pi$ a representation of $G$ by weakly^* continuous isometries acting in a dual Banach space $E$. Given a probability measure $\\mu$ on $G$ we study the Choquet-Deny equation $\\pi(\\mu)x=x$, $x\\in E$. We prove that the solutions of this equation form the range of a projection of norm 1 and can be represented by means of a ``Poisson formula'' on the same boundary space that is used to represent the bounded harmonic functions of the random walk of law $\\mu$. The relation between the space of solutions of the Choquet-Deny equation in $E$ and the space of bounded harmonic functions can be understood in terms of a construction resembling the $W^*$-crossed product and coinciding precisely with the crossed product in the special case of the Choquet-Deny equation in the space $E=B(L^2(G))$ of bounded linear operators on $L^2(G)$. Other general properties of the Choquet-Deny equation in a Banach space are also discussed.

Jaworski, W

2006-01-01

149

On Generalized Strong Vector Variational-Like Inequalities in Banach Spaces  

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Full Text Available The purpose of this paper is to study the solvability for a class of generalized strong vector variational-like inequalities in reflexive Banach spaces. Firstly, utilizing Brouwer's fixed point theorem, we prove the solvability for this class of generalized strong vector variational-like inequalities without monotonicity assumption under some quite mild conditions. Secondly, we introduce the new concept of pseudomonotonicity for vector multifunctions, and prove the solvability for this class of generalized strong vector variational-like inequalities for pseudomonotone vector multifunctions by using Fan's lemma and Nadler's theorem. Our results give an affirmative answer to an open problem proposed by Chen and Hou in 2000, and also extend and improve the corresponding results of Fang and Huang (2006.

Lin Yen-Cherng

2007-01-01

150

On Generalized Strong Vector Variational-Like Inequalities in Banach Spaces  

Directory of Open Access Journals (Sweden)

Full Text Available The purpose of this paper is to study the solvability for a class of generalized strong vector variational-like inequalities in reflexive Banach spaces. Firstly, utilizing Brouwer's fixed point theorem, we prove the solvability for this class of generalized strong vector variational-like inequalities without monotonicity assumption under some quite mild conditions. Secondly, we introduce the new concept of pseudomonotonicity for vector multifunctions, and prove the solvability for this class of generalized strong vector variational-like inequalities for pseudomonotone vector multifunctions by using Fan's lemma and Nadler's theorem. Our results give an affirmative answer to an open problem proposed by Chen and Hou in 2000, and also extend and improve the corresponding results of Fang and Huang (2006.

Lu-Chuan Ceng

2007-04-01

151

Approximation of operators in Banach spaces  

CERN Multimedia

It is a translation of an old paper of mine. We describe the topology tau_p in the space Pi_p(Y,X), for which the closures of convex sets in tau_p and in *-weak topology of the space Pi_p(Y,X) are coincident. Thereafter, we investigate some properties of the space Pi_p, related to this new topology. 2010-remark: Occasionally, the topology is coincides with the lambda_p-topology from the paper "Compact operators which factor through subspaces of l_p", Math. Nachr. 281(2008), 412-423 by Deba Prasad Sinha and Anil Kumar Karn.

Reinov, Oleg I

2010-01-01

152

An explicit example concernig the invariant subspace problem for Banach spaces  

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We simplify the negative solution to the invariant subspace problem for Banach spaces. Developing the ideas of Read we give an explicit example of a continuous linear operator on the Banach space of all absolute summable scalar sequences without nontrivial closed invariant subspaces

S?liwa, Wies?aw

2010-01-01

153

Weak and strong convergence theorems for relatively nonexpansive mappings in Banach spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We first introduce an iterative sequence for finding fixed points of relatively nonexpansive mappings in Banach spaces, and then prove weak and strong convergence theorems by using the notion of generalized projection. We apply these results to the convex feasibility problem and a proximal-type algorithm for monotone operators in Banach spaces.

Matsushita Shin-ya; Takahashi Wataru

2004-01-01

154

Weak and strong convergence theorems for relatively nonexpansive mappings in Banach spaces  

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Full Text Available We first introduce an iterative sequence for finding fixed points of relatively nonexpansive mappings in Banach spaces, and then prove weak and strong convergence theorems by using the notion of generalized projection. We apply these results to the convex feasibility problem and a proximal-type algorithm for monotone operators in Banach spaces.

Wataru Takahashi

2004-03-01

155

Weak and strong convergence theorems for relatively nonexpansive mappings in Banach spaces  

Directory of Open Access Journals (Sweden)

Full Text Available We first introduce an iterative sequence for finding fixed points of relatively nonexpansive mappings in Banach spaces, and then prove weak and strong convergence theorems by using the notion of generalized projection. We apply these results to the convex feasibility problem and a proximal-type algorithm for monotone operators in Banach spaces.

Matsushita Shin-ya

2004-01-01

156

Generation theory for semigroups of holomorphic mappings in Banach spaces  

Directory of Open Access Journals (Sweden)

Full Text Available We study nonlinear semigroups of holomorphic mappings in Banach spaces and their infinitesimal generators. Using resolvents, we characterize, in particular, bounded holomorphic generators on bounded convex domains and obtain an analog of the Hille exponential formula. We then apply our results to the null point theory of semi-plus complete vector fields. We study the structure of null point sets and the spectral characteristics of null points, as well as their existence and uniqueness. A global version of the implicit function theorem and a discussion of some open problems are also included.

Simeon Reich

1996-01-01

157

Iterative solutions of nonlinear equations in smooth Banach spaces  

International Nuclear Information System (INIS)

Let E be a smooth Banach space over the real field, ? not= K is contained in E closed convex and bounded, T:K ? K uniformly continuous and strongly pseudo-contractive. It is proved that the Ishikawa iteration process converges strongly to the unique fixed point of T. Applications of this result to the operator equations Au=f or u+Au=f where A is a strongly accretive mapping of E into itself and under various continuity assumptions on A are also given. (author). 41 refs

1994-01-01

158

Parameter choice in Banach space regularization under variational inequalities  

Science.gov (United States)

The authors study parameter choice strategies for the Tikhonov regularization of nonlinear ill-posed problems in Banach spaces. The effectiveness of any parameter choice for obtaining convergence rates depends on the interplay of the solution smoothness and the nonlinearity structure, and it can be expressed concisely in terms of variational inequalities. Such inequalities are link conditions between the penalty term, the norm misfit and the corresponding error measure. The parameter choices under consideration include an a priori choice, the discrepancy principle as well as the Lepskii principle. For the convenience of the reader, the authors review in an appendix a few instances where the validity of a variational inequality can be established.

Hofmann, Bernd; Math, Peter

2012-10-01

159

Weak and strong solutions for differential equations in Banach spaces  

Energy Technology Data Exchange (ETDEWEB)

In this paper we give a generalization to recent results by using weak and strong measures of noncompactness. For f:[0,T]xE{yields}E with E is a Banach space we prove that, under suitable assumptions, the Cauchy problem (fd((P) (ar((r((c(x(t)=f(t,x(t)),))(c(t/in R: =set membership[0,T],))))(r((c(x(0)=x{sub 0},))(c()))))))) has at least one weak solution furthermore, with certain conditions, the Cauchy problem (P) has a solution. Next under a generalization of the compactness assumptions, we show that (P) has a solution too.

Gomaa, A.M. E-mail: gomaa5@hotmail.com

2003-11-01

160

Square variation of Brownian paths in Banach spaces  

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It is known that if {W(t),   0≤t≤1} is a standard Brownian motion in ℝ then limn→∞∑i=12n|W(i/2n)−W((i−1)/2n)|2=1 almost surely. We generalize this celebrated theorem of Levy to Brownian motion in real separable Banach spaces.

Mou-Hsiung Chang

1982-01-01

 
 
 
 
161

p-adic Banach space operators and adelic Banach space operators  

Directory of Open Access Journals (Sweden)

Full Text Available In this paper, we study non-Archimedean Banach \\(*\\-algebras \\(\\frak{M}_{p}\\ over the \\(p\\-adic number fields \\(\\mathbb{Q}_{p}\\, and \\(\\frak{M}_{\\mathbb{Q}}\\ over the adele ring \\(\\mathbb{A}_{\\mathbb{Q}}\\. We call elements of \\(\\frak{M}_{p}\\, \\(p\\-adic operators, for all primes \\(p\\, respectively, call those of \\(\\frak{M}_{\\mathbb{Q}}\\, adelic operators. We characterize \\(\\frak{M}_{ \\mathbb{Q}}\\ in terms of \\(\\frak{M}_{p}\\'s. Based on such a structure theorem of \\(\\frak{M}_{\\mathbb{Q}}\\, we introduce some interesting \\(p\\-adic operators and adelic operators.

Ilwoo Cho

2014-01-01

162

A note on nonfragmentability of Banach spaces  

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Full Text Available We use Kenderov-Moors characterization of fragmentability to show that if a compact Hausdorff space X with the tree-completeness property contains a disjoint sequences of clopen sets, then (C(X, weak is not fragmented by any metric which is stronger than weak topology. In particular, C(X does not admit any equivalent locally uniformly convex renorming.

S. Alireza Kamel Mirmostafaee

2001-07-01

163

Spectral results for operators commuting with translations on Banach spaces of sequences on Z^k and Z^  

CERN Multimedia

We study the spectrum of multipliers (bounded operators commuting with the shift operator S) on Banach spaces of sequences on Z and the spectrum of operators commuting with the shift on Banach spaces of sequences on Z^+.We generalize the results for multipliers on Banach spaces of sequences on Z^k.

Petkova, Violeta

2011-01-01

164

Independent functions and the geometry of Banach spaces  

Energy Technology Data Exchange (ETDEWEB)

The main objective of this survey is to present the 'state of the art' of those parts of the theory of independent functions which are related to the geometry of function spaces. The 'size' of a sum of independent functions is estimated in terms of classical moments and also in terms of general symmetric function norms. The exposition is centred on the Rosenthal inequalities and their various generalizations and sharp conditions under which the latter hold. The crucial tool here is the recently developed construction of the Kruglov operator. The survey also provides a number of applications to the geometry of Banach spaces. In particular, variants of the classical Khintchine-Maurey inequalities, isomorphisms between symmetric spaces on a finite interval and on the semi-axis, and a description of the class of symmetric spaces with any sequence of symmetrically and identically distributed independent random variables spanning a Hilbert subspace are considered. Bibliography: 87 titles.

Astashkin, Sergey V; Sukochev, Fedor A

2010-12-31

165

Porosity of perturbed optimization problems in Banach spaces  

Science.gov (United States)

Let X be a Banach space and Z a nonempty closed subset of X. Let be a lower semicontinuous function bounded from below. This paper is concerned with the perturbed optimization problem infz[set membership, variant]Z{J(z)+||x-z||}, denoted by (x,J)-inf for x[set membership, variant]X. In the case when X is compactly fully 2-convex, it is proved in the present paper that the set of all points x in X for which there does not exist z0[set membership, variant]Z such that J(z0)+||x-z0||=infz[set membership, variant]Z{J(z)+||x-z||} is a [sigma]-porous set in X. Furthermore, if X is assumed additionally to be compactly locally uniformly convex, we verify that the set of all points x[set membership, variant]XZ0 such that the problem (x,J)-inf fails to be approximately compact, is a [sigma]-porous set in XZ0, where Z0 denotes the set of all z[set membership, variant]Z such that z[set membership, variant]PZ(z). Moreover, a counterexample to which some results of Ni [R.X. Ni, Generic solutions for some perturbed optimization problem in nonreflexive Banach space, J. Math. Anal. Appl. 302 (2005) 417-424] fail is provided.

Li, Chong; Peng, Li Hui

2006-12-01

166

Frechet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces  

CERN Document Server

This book makes a significant inroad into the unexpectedly difficult question of existence of Frchet derivatives of Lipschitz maps of Banach spaces into higher dimensional spaces. Because the question turns out to be closely related to porous sets in Banach spaces, it provides a bridge between descriptive set theory and the classical topic of existence of derivatives of vector-valued Lipschitz functions. The topic is relevant to classical analysis and descriptive set theory on Banach spaces. The book opens several new research directions in this area of geometric nonlinear functional analysi

Lindenstrauss, Joram; Tiaer, Jaroslav

2012-01-01

167

Perturbation of n dimensional AQ - mixed type functional equation via Banach spaces and Banach algebra : Hyers direct and alternative fixed point methods  

Directory of Open Access Journals (Sweden)

Full Text Available In this paper, the authors obtain the general solution and generalized Ulam - Hyers stability of n dimensional additive quadratic functional equation in Banach spaces using direct and fixed point methods. We also investigate the stability of the above equation in Banach algebra using direct and fixed point approach.

M. Arunkumar

2013-12-01

168

Classes of Banach spaces stable and unstable with respect to the opening  

Digital Repository Infrastructure Vision for European Research (DRIVER)

The paper is a complement to the survey: M.I.Ostrovskii "To\\-po\\-lo\\-gies on the set of all subspaces of a Banach space and related questions of Banach space geometry", Quaestiones Math. (to appear). It contains proofs of some results on stability of properties of Banach spaces with respect to the geometric opening stated in the survey without proofs. Some results of the present paper are of independent interest, in particular the description of a predual property of the B...

Ostrovskii, Mikhail I.

1994-01-01

169

Banach spaces without approximation properties of type p  

CERN Multimedia

The main purpose of this note is to show that the question posed in the paper of Sinha D.P. and Karn A.K.("Compact operators which factor through subspaces of $l_p$ Math. Nachr. 281, 2008, 412-423; see the very end of that paper) has a negative answer, and that the answer was known, essentially, in 1985 after the papers "Approximation properties of order p and the existence of non-p-nuclear operators with p-nuclear second adjoints" (Math. Nachr. 109(1982), 125-134) and "Approximation of operators in Banach spaces" (Application of functional analysis in the approximation theory (KGU, Kalinin), 1985, 128-142) by Reinov O.I. have been appeared in 1982 and in 1985 respectively.

Reinov, Oleg

2010-01-01

170

Parameter choice in Banach space regularization under variational inequalities  

International Nuclear Information System (INIS)

The authors study parameter choice strategies for the Tikhonov regularization of nonlinear ill-posed problems in Banach spaces. The effectiveness of any parameter choice for obtaining convergence rates depends on the interplay of the solution smoothness and the nonlinearity structure, and it can be expressed concisely in terms of variational inequalities. Such inequalities are link conditions between the penalty term, the norm misfit and the corresponding error measure. The parameter choices under consideration include an a priori choice, the discrepancy principle as well as the Lepskii principle. For the convenience of the reader, the authors review in an appendix a few instances where the validity of a variational inequality can be established. (paper)

2012-10-01

171

Stroboscopic averaging in Banach spaces: Application to NLS  

Science.gov (United States)

We consider general, highly-oscillatory evolution equations, posed in a Banach space (more precisely high- frequency systems, with one frequency in an infinite-dimensional setting) and we describe an averaging procedure (namely stroboscopic averaging) for which the obtained averaged system respects the intrinsic geometric properties of the original equation. The typical example we have in mind in that of nonlinear PDE's in a high-frequency regime, where only one frequency is present, and the averaged effect of the oscillations in the nonlinearities is to be computed at high order. We apply our results to general nonlinear Schrdinger equations in a high-frequency regime and show that, up to a simple and standard filtering procedure, the obtained results provide a hierarchy of models that approximate the original equations.

Castella, F.; Chartier, Ph.; Mhats, F.; Murua, A.

2012-09-01

172

Characterization of the absolutely summing operators in a Banach space using ?-approximate l_1 sequences  

Directory of Open Access Journals (Sweden)

Full Text Available In this paper we will give a characterization of 1-absolutely summing operators using ?-approximate l_1 sequences. Exactly if (x_n _1^? is ?-approximate l_1 , basic and normalized sequence in Banach space X then every bounded linear operator T from X into Banach space Y is 1-absolutely summing if and only if Y is isomorphic to Hilbert space.

N. L. Braha

2005-05-01

173

Weak convergence of an iterative sequence for accretive operators in Banach spaces  

Directory of Open Access Journals (Sweden)

Full Text Available Let C be a nonempty closed convex subset of a smooth Banach space E and let A be an accretive operator of C into E. We first introduce the problem of finding a point u∈C such that 〈Au,J(v−u〉≥0 for all v∈C, where J is the duality mapping of E. Next we study a weak convergence theorem for accretive operators in Banach spaces. This theorem extends the result by Gol'shteĭn and Tret'yakov in the Euclidean space to a Banach space. And using our theorem, we consider the problem of finding a fixed point of a strictly pseudocontractive mapping in a Banach space and so on.

Wataru Takahashi

2006-06-01

174

Banach-valued Holomorphic Functions on the Maximal Ideal Space of H^\\infty  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We study Banach-valued holomorphic functions defined on open subsets of the maximal ideal space of the Banach algebra H^\\infty of bounded holomorphic functions on the unit disk D\\subset C with pointwise multiplication and supremum norm. In particular, we establish vanishing cohomology for sheaves of germs of such functions and, solving a Banach-valued corona problem for H^\\infty, prove that the maximal ideal space of the algebra H_{\\rm comp}^\\infty (A) of holomorphic functio...

Brudnyi, Alexander

2011-01-01

175

Approximating common fixed points of two asymptotically quasi-nonexpansive mappings in Banach spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

In this paper, we consider a composite iterative algorithm for approximating common fixed points of two nonself asymptotically quasi-nonexpansive mappings and we prove some strong and weak convergence theorems for such mappings in uniformly convex Banach spaces.

2011-01-01

176

Approximating zero points of accretive operators with compact domains in general Banach spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We prove strong convergence theorems of Mann's type and Halpern's type for resolvents of accretive operators with compact domains and apply these results to find fixed points of nonexpansive mappings in Banach spaces.

2005-01-01

177

Random fixed point theorems for nonexpansive and contractive-type random operators on Banach spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

The existence of random fixed points. for nonexpansive and pseudocontractive random multivalued operators defined on unbounded subsets of a Banach space is proved. A random coincidence point theorem for a pair of compatible random multivalued operators is established.

1994-01-01

178

On second-order multivalued impulsive functional differential inclusions in Banach spaces  

Directory of Open Access Journals (Sweden)

Full Text Available A fixed point theorem for condensing maps due to Martelli is used to investigate the existence of solutions to second-order impulsive initial value problem for functional differential inclusions in Banach spaces.

S. K. Ntouyas

2001-12-01

179

Exponential dichotomies for linear discrete-time systems in Banach spaces  

Directory of Open Access Journals (Sweden)

Full Text Available In this paper we investigate some dichotomy concepts for linear difference equations in Banach spaces. Characterizations of these concepts are given. Some illustrating examples clarify the relations between these concepts.

Ioan-Lucian Popa

2012-04-01

180

Fixed point iterations for a class of nonlinear mappings in certain Banach spaces  

International Nuclear Information System (INIS)

It is proved that both the Mann iteration method and the Ishikawa iteration method converge strongly, in real Banach spaces with a certain property, to the unique fixed point of nonlinear mappings belonging to class C. 15 refs

1991-01-01

 
 
 
 
181

Mathematical simulation of almost periodic functions with values in Banach space by means of the multiplicator  

Directory of Open Access Journals (Sweden)

Full Text Available Research of almost periodic functions with values in Banach space proceeds. The concept of the multiplicator by means of which the theorem of integral from almost periodic function is proved is entered.

Kretov M.

2013-01-01

182

Ishikawa iteration process with errors for nonexpansive mappings in uniformly convex Banach spaces  

Directory of Open Access Journals (Sweden)

Full Text Available We shall consider the behaviour of Ishikawa iteration with errors in a uniformly convex Banach space. Then we generalize the two theorems of Tan and Xu without the restrictions that C is bounded and limsupnsn<1.

Li Shenghong

2000-07-01

183

On The Maximal Ideals In The Banach Space Of Quasicontinuous Functions  

Directory of Open Access Journals (Sweden)

Full Text Available In this paper, some interesting properties of Quasicontinuousfunctions are presented. The maximal ideals in the Banach space of bounded real valuedQuasicontinuous functions defined on [0,1] are investigated.

V. Srinivasa Kumar

2013-04-01

184

Under a suitable renorming every nonreflexive Banach space has a finite subset without a Steiner point  

Directory of Open Access Journals (Sweden)

Full Text Available We present a refinement of the recent Borodin's example of a finite set without a Steiner point. Namely, we show that under a suitable renorming such an example exists in every nonreflexive Banach space.

V. Kadets

2011-11-01

185

Convergence rates for an iteratively regularized Newton-Landweber iteration in Banach space  

Science.gov (United States)

In this paper, we provide convergence and convergence rate results for a Newton-type method with a modified version of Landweber iteration as an inner iteration in a Banach space setting. Numerical experiments illustrate the performance of the method.

Kaltenbacher, Barbara; Tomba, Ivan

2013-02-01

186

Controllability of nonlinear differential evolution systems in a separable Banach space  

Directory of Open Access Journals (Sweden)

Full Text Available In this article, we study the controllability of semilinear evolution differential systems with nonlocal initial conditions in a separable Banach space. The results are obtained by using Hausdorff measure of noncompactness and a new calculation method.

Bheeman Radhakrishnan

2012-08-01

187

A class of fractional delay nonlinear integrodifferential controlled systems in Banach spaces  

Science.gov (United States)

We study a class of fractional delay nonlinear integrodifferential controlled systems associated with analytic semigroup in Banach spaces. Existence of ?-mild solutions and optimal controls are obtained. Lastly, an example is presented to illustrate our abstract results.

Wang, JinRong; Zhou, Yong; Wei, W.

2011-10-01

188

Existence and uniqueness of solutions for the fractional integro-differential equations in Banach spaces  

Directory of Open Access Journals (Sweden)

Full Text Available In this article, we established the existence and uniqueness of solutions for fractional integro-differential equations with nonlocal conditions in Banach spaces. Krasnoselskii-Krein-type conditions are used for obtaining the main result.

Yicheng Liu

2009-10-01

189

Impulsive moving mirror model and impulsive differential equations in Banach space.  

Science.gov (United States)

The dependence of vacuum state energy on the distance between the uniformly relatively moving mirrors is used to calculate impulsive differential equations in Banach space. We formulate the problem of moving mirrors, possibly with suddenly change of veloc...

G. Petrov

1992-01-01

190

Approximating zero points of accretive operators with compact domains in general Banach spaces  

Directory of Open Access Journals (Sweden)

Full Text Available We prove strong convergence theorems of Mann's type and Halpern's type for resolvents of accretive operators with compact domains and apply these results to find fixed points of nonexpansive mappings in Banach spaces.

Miyake Hiromichi

2005-01-01

191

Approximating zero points of accretive operators with compact domains in general Banach spaces  

Directory of Open Access Journals (Sweden)

Full Text Available We prove strong convergence theorems of Mann's type and Halpern's type for resolvents of accretive operators with compact domains and apply these results to find fixed points of nonexpansive mappings in Banach spaces.

Wataru Takahashi

2005-04-01

192

Operator self-similar processes on Banach spaces  

Directory of Open Access Journals (Sweden)

Full Text Available Operator self-similar (OSS stochastic processes on arbitrary Banach spaces are considered. If the family of expectations of such a process is a spanning subset of the space, it is proved that the scaling family of operators of the process under consideration is a uniquely determined multiplicative group of operators. If the expectation-function of the process is continuous, it is proved that the expectations of the process have power-growth with exponent greater than or equal to 0, that is, their norm is less than a nonnegative constant times such a power-function, provided that the linear space spanned by the expectations has category 2 (in the sense of Baire in its closure. It is shown that OSS processes whose expectation-function is differentiable on an interval (s0,?, for some s0?1, have a unique scaling family of operators of the form {sH:s>0}, if the expectations of the process span a dense linear subspace of category 2. The existence of a scaling family of the form {sH:s>0} is proved for proper Hilbert space OSS processes with an Abelian scaling family of positive operators.

Mihaela T. Matache

2006-01-01

193

Strong convergence theorems for uniformly L-Lipschitzian mappings in Banach spaces  

International Nuclear Information System (INIS)

Let E be a real reflexive Banach space with uniform Gateaux differentiable norm, K be a nonempty bounded closed and convex subset of E , T : K ? K be a uniformly L-Lipschitzian mapping such that F (T) := {x element of K : Tx = x} ? 0, u element of K be fixed and let {?n}n?0 and {?n}n?0 subset of (0, 1) be such that limn?? ?n = 0 = limn? ? ?n and limn? ?(?n - 1)/ ?n = 0, where ?n ?j=0n ?j and ?j = 1 + ?j?jL. Let Sn := (1 - ?n?n)I + ?n?nTn. It is proved that there exists some integer N0 > 1, such that for each n ? N0, there exists unique xn element of K such that xn = ?nu+(1 -?n) 1/ (n + 1) ?j=0n Sjxn. If ? : E ? R is defined by ? (y) := LIMn vertical bar vertical bar xn -y vertical bar vertical bar2 for all y element of E here LIM denotes a Banach limit, vertical bar vertical bar xn - Txn vertical bar vertical bar ? 0 as n ? ? and Kmin intersection F (T) ? 0, where Kmin := {x element of E : ? (x) = min (u element of K) ? (u) }, then it is proved that {xn} converto a fixed point of T. As an application, it is proved that the iterative process, z0 element of K, zn+1 alpha#nu + (1 - ?n) 1/ (n + 1) ?j=0n Sjzn , n ? 0, under suitable conditions on the iteration parameters, converges strongly to a fixed point of T. (author)

2007-01-01

194

Construction of some generalized inverses of operators between Banach spaces and their selections, perturbations and applications  

Digital Repository Infrastructure Vision for European Research (DRIVER)

In this dissertation, continuous homogeneous selections for the set-valued metric generalized inverses T? of linear operators T in Banach spaces are investigated by means of the methods of geometry of Banach spaces. Necessary and sufficient conditions in order that the set valued metric generalized inverses T? of bounded linear operators T have continuous homogeneous selections are given. The results give an answer to the problem posed by Nashed and Votruba. Secondly, the perturbations of...

Ma, Haifeng

2012-01-01

195

Approximation of Common Fixed Points for Families of Mappings in Banach Space  

Directory of Open Access Journals (Sweden)

Full Text Available In this paper. We introduce a general iterative method for the family of mappings and prove the strong convergence of the new iterative scheme in Banach space. The new iterative method includes the iterative scheme of Khan and Domlo and Fukhar-ud-din [Common fixed points Noor iteration for a finite family of asymptotically quasi-nonexpansive mappings in Banach spaces. J. Math. Anal. Appl. 341 (2008 111]. The results generalize the corresponding results.

Zhiming Cheng

2012-06-01

196

Some classes of rational functions and related Banach spaces  

CERN Document Server

For positive integers d, r, and M, we consider the class of rational functions on real d-dimensional space whose denominators are products of at most r functions of the form 1+Q(x) where each Q is a quadratic form with eigenvalues bounded above by M and below by 1/M. Each numerator is a monic monomial of the same degree as the corresponding denominator. Then we form the Banach space of countable linear combinations of such rational functions with absolutely summable coefficients, normed by the infimum of sums of absolute values of the coefficients. We show that for rational functions whose denominators are rth powers of a specific 1+Q, or differences of two such rational functions with the same numerator, the norm is achieved by and only by the obvious combination of one or two functions respectively. We also find bounds for coefficients in partial-fraction decompositions of some specific rational functions, which in some cases are quite sharp.

Dudley, R M; Wang, Zuoqin; Yang, Fangyun

2007-01-01

197

Skipped Blocking and other Decompositions in Banach spaces  

CERN Document Server

Necessary and sufficient conditions are given for when a sequence of finite dimensional subspaces (X_n) can be blocked to be a skipped blocking decompositon (SBD). The condition is order independent, so permutations of conditional basis, for example can be so blocked. This condition is implied if (X_n) is shrinking, or (X_n) is a permutation of a FDD, or if X is reflexive and (X_n) is separating. A separable space X has PCP, if and only if, every norming decomposition (X_n) can be blocked to be a boundedly complete SBD. Every boundedly complete SBD is a JT-decomposition.

Bellenot, S F

2004-01-01

198

Spectral results for operators commuting with translations on Banach spaces of sequences on Zk and Z+  

Scientific Electronic Library Online (English)

Full Text Available SciELO Chile | Language: English Abstract in spanish Estudiamos el espectro de los multiplicadores (operadores acotados que conmutan con el operador shift ) en un espacio de Banach [...] =24 id="_x0000_i1042" src="http://fbpe/img/cubo/v14n3/art02-03.jpg" alt="http://fbpe/img/cubo/v14n3/art02-03.jpg">de sucesiones en . Dado un multiplicador , probamos que donde es el smbolo de . Obtenemos un resultados similar para el espectro de un operador que conmuta con el shift en un espacio de Banach de sucesiones en . Generalizamos los resultados sobre multiplicadores en espacios de Banach de sucesiones en . Abstract in english We study the spectrum of multipliers (bounded operators commuting with the shift operator ) on a Banach space [...] 51" src="http://fbpe/img/cubo/v14n3/art02-03.jpg" alt="http://fbpe/img/cubo/v14n3/art02-03.jpg">of sequences on . Given a multiplier , we prove that where is the symbol of . We obtain a similar result for the spectrum of an operator commuting with the shift on a Banach space of sequences on . We generalize the results for multipliers on Banach spaces of sequences on .

Petkova, Violeta.

199

Algorithm for Solving a Generalized Mixed Equilibrium Problem with Perturbation in a Banach Space  

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Full Text Available Let B be a real Banach space with the dual space B*. Let ?:B?R?{+?} be a proper functional and let ?:BB?R be a bifunction. In this paper, a new concept of ?-proximal mapping of ? with respect to ? is introduced. The existence and Lipschitz continuity of the ?-proximal mapping of ? with respect to ? are proved. By using properties of the ?-proximal mapping of ? with respect to ?, a generalized mixed equilibrium problem with perturbation (for short, GMEPP is introduced and studied in Banach space B. An existence theorem of solutions of the GMEPP is established and a new iterative algorithm for computing approximate solutions of the GMEPP is suggested. The strong convergence criteria of the iterative sequence generated by the new algorithm are established in a uniformly smooth Banach space B, and the weak convergence criteria of the iterative sequence generated by this new algorithm are also derived in B=H a Hilbert space.

Jen-Chih Yao

2010-01-01

200

Algorithm for Solving a Generalized Mixed Equilibrium Problem with Perturbation in a Banach Space  

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Full Text Available Let be a real Banach space with the dual space . Let be a proper functional and let be a bifunction. In this paper, a new concept of -proximal mapping of with respect to is introduced. The existence and Lipschitz continuity of the -proximal mapping of with respect to are proved. By using properties of the -proximal mapping of with respect to , a generalized mixed equilibrium problem with perturbation (for short, GMEPP is introduced and studied in Banach space . An existence theorem of solutions of the GMEPP is established and a new iterative algorithm for computing approximate solutions of the GMEPP is suggested. The strong convergence criteria of the iterative sequence generated by the new algorithm are established in a uniformly smooth Banach space , and the weak convergence criteria of the iterative sequence generated by this new algorithm are also derived in a Hilbert space.

Kum Sangho

2010-01-01

 
 
 
 
201

Characterization of quasi-Banach spaces which coarsely embed into a Hilbert space  

Digital Repository Infrastructure Vision for European Research (DRIVER)

A map f between two metric spaces (X,d_1) and (Y,d_2) is called a coarse embedding of X into Y if there exist two nondecreasing functions phi_1, phi_2:[0,\\infty) --> [0,\\infty) such that: phi_1(d_1(x,y)) \\leq d_2(f(x),f(y)) \\leq phi_2(d_1(x,y)) for all x, y in X, and phi_1(t) tends to \\infty as t tends to \\infty. We characterize those quasi-Banach spaces that have a coarse embedding into a Hilbert space.

Randrianarivony, N. L.

2004-01-01

202

Nonstationary iterated Tikhonov regularization for ill-posed problems in Banach spaces  

International Nuclear Information System (INIS)

Nonstationary iterated Tikhonov regularization is an efficient method for solving ill-posed problems in Hilbert spaces. However, this method may not produce good results in some situations since it tends to oversmooth solutions and hence destroy special features such as sparsity and discontinuity. By making use of duality mappings and Bregman distance, we propose an extension of this method to the Banach space setting and establish its convergence. We also present numerical simulations which indicate that the method in Banach space setting can produce better results. (paper)

2012-10-01

203

Nonstationary iterated Tikhonov regularization for ill-posed problems in Banach spaces  

Science.gov (United States)

Nonstationary iterated Tikhonov regularization is an efficient method for solving ill-posed problems in Hilbert spaces. However, this method may not produce good results in some situations since it tends to oversmooth solutions and hence destroy special features such as sparsity and discontinuity. By making use of duality mappings and Bregman distance, we propose an extension of this method to the Banach space setting and establish its convergence. We also present numerical simulations which indicate that the method in Banach space setting can produce better results.

Jin, Qinian; Stals, Linda

2012-10-01

204

Convergence Theorems on a New Iteration Process for Two Asymptotically Nonexpansive Nonself-Mappings with Errors in Banach Spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We introduce a new two-step iterative scheme for two asymptotically nonexpansive nonself-mappings in a uniformly convex Banach space. Weak and strong convergence theorems are established for this iterative scheme in a uniformly convex Banach space. The results presented extend and improve the corresponding results of Chidume et al. (2003), Wang (2006), Shahzad (2005), and Thianwan (2008).

2010-01-01

205

Convergence Theorems on a New Iteration Process for Two Asymptotically Nonexpansive Nonself-Mappings with Errors in Banach Spaces  

Directory of Open Access Journals (Sweden)

Full Text Available We introduce a new two-step iterative scheme for two asymptotically nonexpansive nonself-mappings in a uniformly convex Banach space. Weak and strong convergence theorems are established for this iterative scheme in a uniformly convex Banach space. The results presented extend and improve the corresponding results of Chidume et al. (2003, Wang (2006, Shahzad (2005, and Thianwan (2008.

Hukmi Kiziltunc

2010-01-01

206

Banach's and Kannan's fixed point results in fuzzy 2-metric spaces  

Scientific Electronic Library Online (English)

Full Text Available SciELO Chile | Language: English Abstract in english In this paper we establish two common fixed point theorems in fuzzy 2- metric spaces. These theorems are generalizations of the Banach Contraction mapping principle and the Kannan's fixed point theorem respectively in fuzzy 2-metric spaces. [...

Binod, Chandra Tripathy; Paul, Sudipta; Ram Das, Nanda.

207

Solving linear operator equations in Banach spaces non-iteratively by the method of approximate inverse  

International Nuclear Information System (INIS)

The method of approximate inverse is a mollification method for stably solving inverse problems. In its original form it has been developed to solve operator equations in L2-spaces and general Hilbert spaces. We show that the method of approximate inverse can be extended to solve linear, ill-posed problems in Banach spaces. This paper is restricted to function spaces. The method itself consists of evaluations of dual pairings of the given data with reconstruction kernels that are associated with mollifiers and the dual of the operator. We first define what we mean by a mollifier in general Banach spaces and then investigate two settings more exactly: the case of Lp-spaces and the case of the Banach space of continuous functions on a compact set. For both settings we present the criteria turning the method of approximate inverse into a regularization method and prove convergence with rates. As an application we refer to x-ray diffractometry which is a technique of non-destructive testing that is concerned with computing the stress tensor of a specimen. Since one knows that the stress tensor is smooth, x-ray diffractometry can appropriately be modelled by a Banach space setting using continuous functions

2010-08-01

208

Optimal relaxed control of dissipative stochastic partial differential equations in Banach spaces  

CERN Multimedia

We study an optimal relaxed control problem for a class of semilinear stochastic PDEs on Banach spaces perturbed by multiplicative noise and driven by a cylindrical Wiener process. The state equation is controlled through the nonlinear part of the drift coefficient which satisfies a dissipative-type condition with respect to the state variable. The main tools of our study are the factorization method for stochastic convolutions in UMD type-2 Banach spaces and certain compactness properties of the factorization operator and of the class of Young measures on Suslin metrisable control sets.

Brzezniak, Zdzislaw

2010-01-01

209

A New Two-Step Iterative Process with Errors for Common Fixed Points in Banach Spaces  

Directory of Open Access Journals (Sweden)

Full Text Available In this paper, a new two-step iterative scheme with errors is introduced for two asymptotically nonexpansive nonself-mappings. Several convergence theorems are established in real Banach spaces and real uniformly convex Banach spaces. Our theorems improve and extend the results due to Agarwal-O'Regan-Sahu [R.P. Agarwal, Donal O'Regan and D.R. Sahu, Iterative construction of fixed points of nearly asymptotically nonexpansive mappings, J.Nonliear Convex. Anal.8(1(2007 61--79] and many other papers.

Esref Turkmen

2011-12-01

210

The approximate inverse in action: IV. Semi-discrete equations in a Banach space setting  

Science.gov (United States)

This article concerns the method of approximate inverse to solve semi-discrete, linear operator equations in Banach spaces. Semi-discrete means that we search for a solution in an infinite-dimensional Banach space having only a finite number of data available. In this sense the situation is applicable to a large variety of applications where a measurement process delivers a discretization of an infinite-dimensional data space. The method of approximate inverse computes scalar products of the data with pre-computed reconstruction kernels which are associated with mollifiers and the dual of the model operator. The convergence, approximation power and regularization property of this method when applied to semi-discrete operator equations in Hilbert spaces has been investigated in three prequels to this paper. Here we extend these results to a Banach space setting. We prove convergence and stability for general Banach spaces and reproduce the results specifically for the integration operator acting on the space of continuous functions.

Schuster, T.; Rieder, A.; Schpfer, F.

2012-10-01

211

The approximate inverse in action: IV. Semi-discrete equations in a Banach space setting  

International Nuclear Information System (INIS)

This article concerns the method of approximate inverse to solve semi-discrete, linear operator equations in Banach spaces. Semi-discrete means that we search for a solution in an infinite-dimensional Banach space having only a finite number of data available. In this sense the situation is applicable to a large variety of applications where a measurement process delivers a discretization of an infinite-dimensional data space. The method of approximate inverse computes scalar products of the data with pre-computed reconstruction kernels which are associated with mollifiers and the dual of the model operator. The convergence, approximation power and regularization property of this method when applied to semi-discrete operator equations in Hilbert spaces has been investigated in three prequels to this paper. Here we extend these results to a Banach space setting. We prove convergence and stability for general Banach spaces and reproduce the results specifically for the integration operator acting on the space of continuous functions. (paper)

2012-10-01

212

Existence of solutions and convergence analysis for a system of quasivariational inclusions in Banach spaces  

Directory of Open Access Journals (Sweden)

Full Text Available Abstract In order to unify some variational inequality problems, in this paper, a new system of generalized quasivariational inclusion (for short, (SGQVI is introduced. By using Banach contraction principle, some existence and uniqueness theorems of solutions for (SGQVI are obtained in real Banach spaces. Two new iterative algorithms to find the common element of the solutions set for (SGQVI and the fixed points set for Lipschitz mappings are proposed. Convergence theorems of these iterative algorithms are established under suitable conditions. Further, convergence rates of the convergence sequences are also proved in real Banach spaces. The main results in this paper extend and improve the corresponding results in the current literature. 2000 MSC: 47H04; 49J40.

Chen Jia-wei

2011-01-01

213

Ergodic BSDEs and Optimal Ergodic Control in Banach Spaces  

CERN Multimedia

In this paper we introduce a new kind of Backward Stochastic Differential Equations, called ergodic BSDEs, which arise naturally in the study of optimal ergodic control. We study the existence, uniqueness and regularity of solution to ergodic BSDEs. Then we apply these results to the optimal ergodic control of a Banach valued stochastic state equation. We also establish the link between the ergodic BSDEs and the associated Hamilton-Jacobi-Bellman equation. Applications are given to ergodic control of stochastic partial differential equations.

Fuhrman, Marco; Tessitore, Gianmario

2007-01-01

214

FOREWORD: Tackling inverse problems in a Banach space environment: from theory to applications Tackling inverse problems in a Banach space environment: from theory to applications  

Science.gov (United States)

Inverse problems can usually be modelled as operator equations in infinite-dimensional spaces with a forward operator acting between Hilbert or Banach spacesa formulation which quite often also serves as the basis for defining and analyzing solution methods. The additional amount of structure and geometric interpretability provided by the concept of an inner product has rendered these methods amenable to a convergence analysis, a fact which has led to a rigorous and comprehensive study of regularization methods in Hilbert spaces over the last three decades. However, for numerous problems such as x-ray diffractometry, certain inverse scattering problems and a number of parameter identification problems in PDEs, the reasons for using a Hilbert space setting seem to be based on conventions rather than an appropriate and realistic model choice, so often a Banach space setting would be closer to reality. Furthermore, non-Hilbertian regularization and data fidelity terms incorporating a priori information on solution and noise, such as general Lp-norms, TV-type norms, or the Kullback-Leibler divergence, have recently become very popular. These facts have motivated intensive investigations on regularization methods in Banach spaces, a topic which has emerged as a highly active research field within the area of inverse problems. Meanwhile some of the most well-known regularization approaches, such as Tikhonov-type methods requiring the solution of extremal problems, and iterative ones like the Landweber method, the Gauss-Newton method, as well as the approximate inverse method, have been investigated for linear and nonlinear operator equations in Banach spaces. Convergence with rates has been proven and conditions on the solution smoothness and on the structure of nonlinearity have been formulated. Still, beyond the existing results a large number of challenging open questions have arisen, due to the more involved handling of general Banach spaces and the larger variety of concrete instances with special properties. The aim of this special section is to provide a forum for highly topical ongoing work in the area of regularization in Banach spaces, its numerics and its applications. Indeed, we have been lucky enough to obtain a number of excellent papers both from colleagues who have previously been contributing to this topic and from researchers entering the field due to its relevance in practical inverse problems. We would like to thank all contributers for enabling us to present a high quality collection of papers on topics ranging from various aspects of regularization via efficient numerical solution to applications in PDE models. We give a brief overview of the contributions included in this issue (here ordered alphabetically by first author). In their paper, Iterative regularization with general penalty termtheory and application to L1 and TV regularization, Radu Bot and Torsten Hein provide an extension of the Landweber iteration for linear operator equations in Banach space to general operators in place of the inverse duality mapping, which corresponds to the use of general regularization functionals in variational regularization. The L? topology in data space corresponds to the frequently occuring situation of uniformly distributed data noise. A numerically efficient solution of the resulting Tikhonov regularization problem via a Moreau-Yosida appriximation and a semismooth Newton method, along with a ?-free regularization parameter choice rule, is the topic of the paper L? fitting for inverse problems with uniform noise by Christian Clason. Extension of convergence rates results from classical source conditions to their generalization via variational inequalities with a priori and a posteriori stopping rules is the main contribution of the paper Regularization of linear ill-posed problems by the augmented Lagrangian method and variational inequalities by Klaus Frick and Markus Grasmair, again in the context of some iterative method. A powerful tool for proving convergence rates of Tikhonov type but also othe

Schuster, Thomas; Hofmann, Bernd; Kaltenbacher, Barbara

2012-10-01

215

Khinchin inequality and Banach-Saks type properties in rearrangement-invariant spaces  

CERN Document Server

{\\it We study the class of all rearrangement-invariant (=r.i.) function spaces $E$ on $[0,1]$ such that there exists $00$ does not depend on $n$. We completely characterize all Lorentz spaces having this property and complement classical results of Rodin and Semenov for Orlicz spaces $exp(L_p)$, $p\\ge 1$. We further apply our results to the study of Banach-Saks index sets in r.i. spaces.

Sukochev, F

2010-01-01

216

Block Iterative Methods for a Finite Family of Relatively Nonexpansive Mappings in Banach Spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Using the convex combination based on Bregman distances due to Censor and Reich, we define an operator from a given family of relatively nonexpansive mappings in a Banach space. We first prove that the fixed-point set of this operator is identical to the set of all common fixed points of the mappings. Next, using this operator, we construct an iterative sequence to approximate common fixed points of the family. We finally apply our results to a convex feasibility problem in Banach spa...

Fumiaki Kohsaka; Wataru Takahashi

2007-01-01

217

Psi-exponential dichotomy for linear differential equations in a Banach space  

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Full Text Available In this article we extend the concept psi-exponential and psi-ordinary dichotomies for homogeneous linear differential equations in a Banach space. With these two concepts we prove the existence of psi-bounded solutions of the appropriate inhomogeneous equation. A roughness of the psi-dichotomy is also considered.

Atanaska Georgieva

2013-07-01

218

Existence results for second order functional differential and integrodifferential inclusions in Banach spaces  

Directory of Open Access Journals (Sweden)

Full Text Available In this paper we investigate the existence of solutions on a compact interval to second order initial value problems for functional differential and integrodifferential inclusions in Banach spaces. We shall make use of a fixed point theorem for condensing maps due to Martelli.

M. Benchohra

2001-12-01

219

On a nonlinear integrodifferential evolution inclusion with nonlocal initial conditions in Banach spaces  

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Full Text Available In this paper, we discuss the existence results for a class of nnlinear integrodifferential evolution inclusions with nonlocal initial conditions in Banach spaces. Our results are based on a fixed point theorem for condensing maps due to Martelli and the resolvent operators combined with approximation techniques.

Zuomao Yan

2012-01-01

220

Existence results for second-order neutral functional differential and integrodifferential inclusions in Banach spaces  

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Full Text Available In this paper, we investigate the existence of mild solutions on a compact interval to second order neutral functional differential and integrodifferential inclusions in Banach spaces. The results are obtained by using the theory of continuous cosine families and a fixed point theorem for condensing maps due to Martelli.

Haeng Joo Lee

2002-11-01

 
 
 
 
221

Existence results for neutral functional differential and integrodifferential inclusions in Banach spaces  

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Full Text Available In this paper we investigate the existence of solutions on a compact interval for the first and second order initial-value problems for neutral functional differential and integrodifferential inclusions in Banach spaces. We shall use of a fixed point theorem for condensing maps introduced by Martelli.

Mouffak Benchohra

2000-03-01

222

Analysis of integrodifferential control system with pulse-width modulated sampler on Banach spaces  

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Full Text Available This paper studies steady-state control and stability for a class of integrodifferential control system with pulse-width modulated sampler on Banach spaces. The existence and stability of the steady-state for the integrodifferential control system with pulse-width modulated sampler are given. An example is given to illustrate the theory.

JinRong Wang

2012-01-01

223

Analogues of the Markov and Bernstein inequalities on convex bodies in Banach spaces  

Energy Technology Data Exchange (ETDEWEB)

We obtain analogues of the A.A. Markov and Bernstein inequalities for algebraic polynomials on convex bounded closed bodies in Banach spaces. For centrally symmetric bodies we establish an exact estimate in Markov's inequality, an estimate in Bernstein's inequality that is asymptotically exact for polynomials on the ball, and estimates for the norms of higher derivatives.

Skalyga, V I

1998-04-30

224

On the rate of convergence of bootstrapped means in a Banach space  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We establish the complete convergence for arrays of Banach space valued random elements. This result is applied to bootstrapped means of random elements to obtain their strong consistency and is derived in the spirit of Baum-Katz/Hsu-Robbins/Spitzer type convergence.

Ejaz Ahmed, S.; -c Hu, T.; Volodin, Andrei I.

2001-01-01

225

Convergence rates for an iteratively regularized NewtonLandweber iteration in Banach space  

International Nuclear Information System (INIS)

In this paper, we provide convergence and convergence rate results for a Newton-type method with a modified version of Landweber iteration as an inner iteration in a Banach space setting. Numerical experiments illustrate the performance of the method. (paper)

2013-02-01

226

Mixed Monotone Iterative Technique for Impulsive Periodic Boundary Value Problems in Banach Spaces  

Directory of Open Access Journals (Sweden)

Full Text Available This paper deals with the existence of -quasi-solutions for impulsive periodic boundary value problems in an ordered Banach space . Under a new concept of upper and lower solutions, a new monotone iterative technique on periodic boundary value problems of impulsive differential equations has been established. Our result improves and extends some relevant results in abstract differential equations.

Chen Pengyu

2011-01-01

227

Mixed Monotone Iterative Technique for Impulsive Periodic Boundary Value Problems in Banach Spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

This paper deals with the existence of -quasi-solutions for impulsive periodic boundary value problems in an ordered Banach space . Under a new concept of upper and lower solutions, a new monotone iterative technique on periodic boundary value problems of impulsive differential equations has been established. Ou...

2011-01-01

228

Approximation Methods for Common Fixed Points of Mean Nonexpansive Mapping in Banach Spaces  

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Full Text Available Let be a uniformly convex Banach space, and let be a pair of mean nonexpansive mappings. In this paper, it is proved that the sequence of Ishikawa iterations associated with and converges to the common fixed point of and .

Li Yongjin

2008-01-01

229

Stable Coexistence and Bi-stability for Competitive Systems on Ordered Banach Spaces  

Science.gov (United States)

Autonomous and asymptotically autonomous semiflows modeling two species competition are studied which are strongly order preserving on a convex subset of a Banach space with competitive order. Conditions are derived for stable coexistence, bi-stability, and competitive exclusion. A complete classification of all possible outcomes is obtained in case that there is at most one positive steady state representing coexistence of both species.

Smith, H. L.; Thieme, H. R.

230

Strong Convergence Theorems for Fixed Points of Asymptotically Nonexpansive Mappings in Uniformly Smooth Banach Spaces  

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Full Text Available In this work, we establish strong convergence of the improved modified three-step iteration methods for asymptotically nonexpansive operators in uniformly smooth and convex Banach spaces. Our results generalize the previous results of Schu [10], Osilike and Aniagbosor [5], Xu and Noor [13], as well as Owojori and Imoru [7] among others.

Olusegun O. Owojori

2005-01-01

231

Strong Convergence Theorems for Fixed Points of Asymptotically Nonexpansive Mappings in Uniformly Smooth Banach Spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

In this work, we establish strong convergence of the improved modified three-step iteration methods for asymptotically nonexpansive operators in uniformly smooth and convex Banach spaces. Our results generalize the previous results of Schu [10], Osilike and Aniagbosor [5], Xu and Noor [13], as well as Owojori and Imoru [7] among others.

Owojori, Olusegun O.

2005-01-01

232

Extremal solutions to a class of multivalued integral equations in Banach space  

Directory of Open Access Journals (Sweden)

Full Text Available We consider a nonlinear Volterra integral inclusion in a Banach space. We establish the existence of extremal integral solutions, and we show that they are dense in the solution set of the original equation. As an important application, we obtain a ?bang-bang? theorem for a class of nonlinear, infinite dimensional control systems.

Sergiu Aizicovici

1992-01-01

233

On the rate of convergence of bootstrapped means in a Banach space  

Directory of Open Access Journals (Sweden)

Full Text Available We establish the complete convergence for arrays of Banach space valued random elements. This result is applied to bootstrapped means of random elements to obtain their strong consistency and is derived in the spirit of Baum-Katz/Hsu-Robbins/Spitzer type convergence.

Andrei I. Volodin

2001-03-01

234

ON THE ALGEBRAIC DIMENSION OF BANACH SPACES OVER NON-ARCHIMEDEAN VALUED FIELDS OR ARBITRARY RANK  

Scientific Electronic Library Online (English)

Full Text Available SciELO Chile | Language: English Abstract in english Let K be a complete non-archimedean valued field of any rank, and let E be a K-Banach space with a countable topological base. We determine the algebraic dimension of E (2.3, 2.4, 3.1). [...

HERMINIA, OCHSENIUS; W. H., SCHIKHOF.

235

A Coefficient Related to Some Geometric Properties of a Banach Space  

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Full Text Available We introduce a new coefficient as a generalization of the modulus of smoothness and Pythagorean modulus of Banach space X. Some basic properties of this new coefficient are investigated. Moreover, some sufficient conditions which imply normal structure are presented.

Zhanfei Zuo

2009-01-01

236

Generalized Bohl-Perron principle for differential equations with delay in a Banach spaces  

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Full Text Available We consider a linear homogeneous functional differential equation with delay in a Banach space. It is proved that if the corresponding non-homogeneous equation, with an arbitrary free term bounded on the positive half-line and with the zero initial condition, has a bounded solution, then the considered homogeneous equation is exponentially stable.

Michael Gil'

2013-06-01

237

A Coefficient Related to Some Geometric Properties of a Banach Space  

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Full Text Available Abstract We introduce a new coefficient as a generalization of the modulus of smoothness and Pythagorean modulus of Banach space . Some basic properties of this new coefficient are investigated. Moreover, some sufficient conditions which imply normal structure are presented.

Zuo Zhanfei

2009-01-01

238

Fixed point for asymptotically pointwise nonexpansive mapping in Banach space which has Frechet differential norm  

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Full Text Available Let X be a uniformly convex Banach space which has Frechet differentiablenorm, T : C ? C an asymptotically pointwise nonexpensivemapping where C is bounded, closed and convex subset of X.In this paper, we prove that generalized Mann process converge weaklyto fixed point of T.

G. Khalilzadeh

2013-01-01

239

Bound and periodic solutions of the Riccati equation in Banach space  

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Full Text Available An abstract, nonlinear, differential equation in Banach space is considered. Conditions are presented for the existence of bounded solutions of this equation with a bounded right side, and also for the existence of stationary (periodic solutions of this equation with a stationary (periodic process in the right side.

A. Ya. Dorogovtsev

1995-01-01

240

Stability, Periodicity, and Almost Periodicity of Solutions of Nonlinear Differential Equations in Banach Spaces.  

Science.gov (United States)

A study is made of a differential equation of the form dX/dt + UX = F(t,X, lambda) in a Banach space. The cases of a bounded linear Operator U with spectrum in the right half plane and an unbounded closed linear operator U with dense domain satisfying con...

C. T. Taam

1966-01-01

 
 
 
 
241

Asymptotic behaviour of the solutions of Schroedinger equation with impulse effect in a Banach space  

International Nuclear Information System (INIS)

The present paper studies the asymptotic behaviour of the solutions of linear homogeneous differential Schroedinger equation with impulse effect in a Banach space and finds a dependence between their asymptotic behaviour and the spectrum of the linear Hamiltonian operator. 6 refs

1992-01-01

242

Terminal value problems of impulsive integro-differential equations in Banach spaces  

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Full Text Available This paper uses cone theory and the monotone iterative technique to investigate the existence of minimal nonnegative solutions of terminal value problems for first order nonlinear impulsive integro-differential equations of mixed type in a Banach space.

Dajun Guo

1997-01-01

243

On non-absolute functional Volterra integral equations and impulsive differential equations in ordered Banach spaces  

Directory of Open Access Journals (Sweden)

Full Text Available In this article we derive existence and comparison results for discontinuous non-absolute functional integral equations of Volterra type in an ordered Banach space which has a regular order cone. The obtained results are then applied to first-order impulsive differential equations.

Seppo Seikkala

2008-08-01

244

Positive Solutions for Impulsive Equations of Third Order in Banach Space  

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Full Text Available Using the fixed-point theorem, this paper is devoted to study the multiple and single positive solutions of third-order boundary value problems for impulsive differential equations in ordered Banach spaces. The arguments are based on a specially constructed cone. At last, an example is given to illustrate the main results.

Cai Jingjing

2010-01-01

245

Convergence to Compact Sets of Inexact Orbits of Nonexpansive Mappings in Banach and Metric Spaces  

Directory of Open Access Journals (Sweden)

Full Text Available We study the influence of computational errors on the convergence to compact sets of orbits of nonexpansive mappings in Banach and metric spaces. We first establish a convergence theorem assuming that the computational errors are summable and then provide examples which show that the summability of errors is necessary for convergence.

2009-02-01

246

Convergence to Compact Sets of Inexact Orbits of Nonexpansive Mappings in Banach and Metric Spaces  

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Full Text Available We study the influence of computational errors on the convergence to compact sets of orbits of nonexpansive mappings in Banach and metric spaces. We first establish a convergence theorem assuming that the computational errors are summable and then provide examples which show that the summability of errors is necessary for convergence.

Pustylnik Evgeniy

2008-01-01

247

Weak and strong convergence theorems for nonexpansive semigroups in Banach spaces  

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Full Text Available We introduce an implicit iterative process for a nonexpansive semigroup and then we prove a weak convergence theorem for the nonexpansive semigroup in a uniformly convex Banach space which satisfies Opial's condition. Further, we discuss the strong convergence of the implicit iterative process.

Takahashi Wataru

2005-01-01

248

Weak and strong convergence theorems for nonexpansive semigroups in Banach spaces  

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Full Text Available We introduce an implicit iterative process for a nonexpansive semigroup and then we prove a weak convergence theorem for the nonexpansive semigroup in a uniformly convex Banach space which satisfies Opial's condition. Further, we discuss the strong convergence of the implicit iterative process.

Wataru Takahashi

2005-10-01

249

A new composite implicit iterative process for a finite family of nonexpansive mappings in Banach spaces  

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Full Text Available The purpose of this paper is to study the weak and strong convergence of implicit iteration process with errors to a common fixed point for a finite family of nonexpansive mappings in Banach spaces. The results presented in this paper extend and improve the corresponding results of Chang and Cho (2003, Xu and Ori (2001, and Zhou and Chang (2002.

Jing Lu

2006-11-01

250

Mild Solutions for Nonlocal Impulsive Fractional Semilinear Differential Inclusions with Delay in Banach Spaces  

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Full Text Available In this paper, we give various existence results concerning the existence of mild solutions for nonlocal impulsive differential inclusions with delay and of fractional order in Caputo sense in Banach space. We consider the case when the values of the orient field are convex as well as nonconvex. Our obtained results improve and generalize many results proved in recent papers.

Ahmed Gamal Ibrahim

2013-07-01

251

Approximating common fixed points of two asymptotically quasi-nonexpansive mappings in Banach spaces  

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Full Text Available In this paper, we consider a composite iterative algorithm for approximating common fixed points of two nonself asymptotically quasi-nonexpansive mappings and we prove some strong and weak convergence theorems for such mappings in uniformly convex Banach spaces.

Isa Yildirim

2011-03-01

252

Strict convexity of absolute norms on and direct sums of banach spaces  

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Full Text Available We show that an absolute normalized norm on is strictly convex if and only if the corresponding convex function on is strictly convex. In this context the monotonicity property of these norms is discussed. We also introduce the notion of the direct sum of Banach spaces and equipped with the associated norm with and characterize the strict convexity of .

Kato Mikio

2002-01-01

253

Space charge equation calculations for the reflex triode  

International Nuclear Information System (INIS)

The Poisson equation solution of the space charge problem for the reflex triode is reviewed and illustrated with a number of examples. The numerical calculation technique for obtaining these results is briefly described. The results show that the characteristics of the triode are strong functions of the reflex-electron kinetic-energy spectrum, especially of the high-energy electrons

1976-01-01

254

On ultrapowers of Banach spaces of type $\\mathscr L_\\infty$  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We prove that no ultraproduct of Banach spaces via a countably incomplete ultrafilter can contain $c_0$ complemented. This shows that a "result" widely used in the theory of ultraproducts is wrong. We then amend a number of results whose proofs had been infected by that statement. In particular we provide proofs for the following statements: (i) All $M$-spaces, in particular all $C(K)$-spaces, have ultrapowers isomorphic to ultrapowers of $c_0$, as well as all their compleme...

Avile?s, Antonio; Sa?nchez, Fe?lix Cabello; Castillo, Jesu?s M. F.; Gonza?lez, Manuel; Moreno, Yolanda

2013-01-01

255

Convergence rates for regularization of ill-posed problems in Banach spaces by approximate source conditions  

International Nuclear Information System (INIS)

In this paper we deal with convergence rates for regularizing ill-posed problems with operator mapping from a Hilbert space into a Banach space. Since we cannot transfer the well-established convergence rates theory in Hilbert spaces, only few convergence rates results are known in the literature for this situation. Therefore we present an alternative approach for deriving convergence rates. Hereby we deal with so-called distance functions which quantify the violation of a reference source condition. With the aid of these functions we present error bounds and convergence rates for regularized solutions of linear and nonlinear problems when the reference source condition is not satisfied. We show that the approach of applying distance functions carries over the idea of considering generalized source conditions in Hilbert spaces to inverse problems in Banach spaces in a natural way. Introducing this topic for linear ill-posed problems we additionally show that this theory can be easily extended to nonlinear problems

2008-08-01

256

Spectral dilation of L(B,H)-valued measures and its application to stationary dilation for Banach space valued processes  

Science.gov (United States)

Let B be a Banach space and H and K to Hilbert spaces. The spectral dilation of L(B,H)-valued measures is studied and it is shown that the recent results of Makagon and Salehi (1986) and Rosenberg (1982) on the dilation of L(K,H)-valued measures can be extended to hold for the general Banach space setting of L(B,H)-valued measures. These L(B,H)-valued measures are closely connected to the Banach space valued processes. This connection is recalled and as application of spectral dilation of L(B,H)-valued measures the well known stationary dilation results for scalar valued processes is extended to the case of Banach space valued processes.

Miamee, A. G.

1989-01-01

257

Domains of uniqueness for $C_0$-semigroups on the dual of a Banach space  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Let $({\\cal X},\\|\\:.\\:\\|)$ be a Banach space. In general, for a $C_0$-semigroup \\semi on $({\\cal X},\\|\\:.\\:\\|)$, its adjoint semigroup \\semia is no longer strongly continuous on the dual space $({\\cal X}^{*},\\|\\:.\\:\\|^{*})$. Consider on ${\\cal X}^{*}$ the topology of uniform convergence on compact subsets of $({\\cal X},\\|\\:.\\:\\|)$ denoted by ${\\cal C}({\\cal X}^{*},{\\cal X})$, for which the usual semigroups in literature becomes $C_0$-semigroups.\\\\ The main purpose of this paper is to prove th...

Lemle, Ludovic Dan

2008-01-01

258

On LandweberKaczmarz methods for regularizing systems of ill-posed equations in Banach spaces  

International Nuclear Information System (INIS)

In this paper, iterative regularization methods of LandweberKaczmarz type are considered for solving systems of ill-posed equations modeled (finitely many) by operators acting between Banach spaces. Using assumptions of uniform convexity and smoothness on the parameter space, we are able to prove a monotony result for the proposed method, as well as to establish convergence (for exact data) and stability results (in the noisy data case). (paper)

2012-10-01

259

Algorithm for Solving a Generalized Mixed Equilibrium Problem with Perturbation in a Banach Space  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Let B be a real Banach space with the dual space B*. Let ?:B?R?{+?} be a proper functional and let ?:BB?R be a bifunction. In this paper, a new concept of ?-proximal mapping of ? with respect to ? is introduced. The existence and Lipschitz continuity of the ?-proximal mapping of ? with respect to ? are proved. By using properties of the ?-proximal mapping of ? with respect ...

Lu-Chuan Ceng; Sangho Kum; Jen-Chih Yao

2010-01-01

260

A fixed point theorem for a class of differentiable stable operators in banach spaces  

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Full Text Available We study Frèchet differentiable stable operators in real Banach spaces. We present the theory of linear and nonlinear stable operators in a systematic way and prove solvability theorems for operator equations with differentiable expanding operators. In addition, some relations to the theory of monotone operators in Hilbert spaces are discussed. Using the obtained solvability results, we formulate the corresponding fixed point theorem for a class of nonlinear expanding operators.

Vadim Azhmyakov

2006-04-01

 
 
 
 
261

A fixed point theorem for a class of differentiable stable operators in banach spaces  

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Full Text Available We study Frchet differentiable stable operators in real Banach spaces. We present the theory of linear and nonlinear stable operators in a systematic way and prove solvability theorems for operator equations with differentiable expanding operators. In addition, some relations to the theory of monotone operators in Hilbert spaces are discussed. Using the obtained solvability results, we formulate the corresponding fixed point theorem for a class of nonlinear expanding operators.

Azhmyakov Vadim

2006-01-01

262

A general approach to narrow operators and rich subspaces of Banach spaces  

CERN Document Server

Let $X$ be a Banach space. We introduce a formal approach which seems to be useful in the study of those properties of operators on $X$ which depend only on the norms of elements. This approach is applied to the Daugavet equation for norms of operators; in particular we develop a general theory of narrow operators and rich subspaces of $X$ previously studied in the context of the classical spaces $C(K)$ and $L_1(\\mu)$.

Kadets, V; Werner, D; Kadets, Vladimir; Shvidkoy, Roman; Werner, Dirk

2000-01-01

263

Hahn-Banach operators  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We consider real spaces only. Definition. An operator $T:X\\to Y$ between Banach spaces $X$ and $Y$ is called a Hahn-Banach operator if for every isometric embedding of the space $X$ into a Banach space $Z$ there exists a norm-preserving extension $\\tilde T$ of $T$ to $Z$. A geometric property of Hahn-Banach operators of finite rank acting between finite-dimensional normed spaces is found. This property is used to characterize pairs of finite-dimensional normed spaces ...

Ostrovskii, M. I.

2002-01-01

264

Convergence rates and finite-dimensional approximations for nonlinear ill-posed problems involving monotone operators in Banach spaces.  

Science.gov (United States)

The purpose of this paper is to investigate convergence rates for an operator version of Tikhonov regularization constructed by dual mapping for nonlinear ill-posed problems involving monotone operators in real reflective Banach spaces. The obtained resul...

Nguyen Buong

1992-01-01

265

Existence results for differential inclusions with nonlinear growth conditions in Banach spaces.  

Science.gov (United States)

In the Banach space setting, the existence of viable solutions for differential inclusions with nonlinear growth; that is, x()(t) ? a.e. on I, x(t) ? S, ?t ? I, x(0) = x? ? S, (?), where S is a closed subset in a Banach space X, I = [0, T], (T > 0), F : I S ? X, is an upper semicontinuous set-valued mapping with convex values satisfying F(t, x) ? c(t)(||x|| + ||x|| (p)K, ?(t, x) ? I S, where p ? ?, with p ? 1, and c ? C([0, T], ?(+)). The existence of solutions for nonconvex sweeping processes with perturbations with nonlinear growth is also proved in separable Hilbert spaces. PMID:24382470

Bounkhel, Messaoud

2013-01-01

266

Existence of equilibrium point for noncooperative differential game in banach space  

Science.gov (United States)

The existence of the e-equilibrium point for the class of the piecewise-programmed strategies in the noncooperative n-person differential game in the finite-dimensional Euclidean space was proved in [4]. In this paper the results of [4] are generalized to the noncooperative n-person differential game in Banach space. The dynamics of the players is described by the initial value problem for the parabolic operator-differential equation involving Dirac measure. The existence of the ?-equilibrium point for the n-person differential game in Banach space with the separated dynamics of the players and continuous payoff functions depending on a game trajectory is proved in this paper.

Troeva, Marianna

2012-09-01

267

A Hybrid Iterative Scheme for Equilibrium Problems, Variational Inequality Problems, and Fixed Point Problems in Banach Spaces  

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Full Text Available The purpose of this paper is to introduce a new hybrid projection algorithm for finding a common element of the set of solutions of the equilibrium problem and the set of the variational inequality for an inverse-strongly monotone operator and the set of fixed points of relatively quasi-nonexpansive mappings in a Banach space. Then we show a strong convergence theorem. Using this result, we obtain some applications in a Banach space.

Prasit Cholamjiak

2009-01-01

268

On smooth approximation and extension on Banach spaces and applications to Banach-Finsler manifolds = Sobre aproximacin y extensin suave en espacios de Banach y aplicaciones a variedades Banach-Finsler  

Digital Repository Infrastructure Vision for European Research (DRIVER)

El marco de esta memoria es la teora de diferenciabilidad en espacios de Banach y en variedades de tipo Banach-Finsler. En ella nos ocupamos de varias cuestiones diferentes que, como iremos viendo, estn muy relacionadas entre s. El primer problema que abordamos trata de caracterizar los espacios de Banach separables donde existen funciones meseta diferenciables que localmente dependen de un nmero finito de coordenadas. Recordemos que una funcin meseta definida en un espacio de Banac...

Sa?nchez Gonza?lez, Luis Francisco

2012-01-01

269

Convergence theorems of common elements for mixed equilibrium problems, variational inequality problems and fixed point problems in Banach spaces  

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Full Text Available In this paper, a hybrid iterative scheme is introduced for theapproximation method for finding a common element of the set of mixed equilibrium problems, variational inequality problems and fixed point problems of two quasi-$phi$-nonexpansive mappings ina real uniformly convex and uniformly smooth Banach space. Then, we obtain a strong convergence theorem for the sequence generated by those process in Banach spaces. Moreover, we obtain new resultfor finding a zero point of maximal monotone operators in a Banach space. Our results improve and extend the corresponding results announced by Takahashi and Zembayashi [Strong and weak convergencetheorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces, Nonlinear Anal. 70 (2009 45--57.] Qin, Cho and Kang [Convergence theorems of common elements forequilibrium problems and fixed point problems in Banach spaces, J. Comput. Appl. Math., 225 (2009, 20--30.] Wattanawitoon and Kumam [Strong convergence theorems by a new hybrid projection algorithmfor fixed point problems and equilibrium problems of tworelatively quasi-nonexpansive mappings, Nonlinear Anal: Hybrid Systems. 3 (2009 11--20.] Cholamjiak [A hybrid iterative scheme for equilibrium problems, variational inequality problems and fixed point problems in Banach spaces, Fixed Point Theory Appl., (2009, Article ID 719360, 18 pages] and many authors.

Kriengsak Wattanawitoon

2011-01-01

270

From Hahn-Banach to monotonicity  

CERN Document Server

In this new edition of LNM 1693 the essential idea is to reduce questions on monotone multifunctions to questions on convex functions. However, rather than using a big convexification of the graph of the multifunction and the minimax techniquefor proving the existence of linear functionals satisfying certain conditions, the Fitzpatrick function is used. The journey begins with a generalization of the Hahn-Banach theorem uniting classical functional analysis, minimax theory, Lagrange multiplier theory and convex analysis and culminates in a survey of current results on monotone multifunctions on a Banach space. The first two chapters are aimed at students interested in the development of the basic theorems of functional analysis, which leads painlessly to the theory of minimax theorems, convex Lagrange multiplier theory and convex analysis. The remaining five chapters are useful for those who wish to learn about the current research on monotone multifunctions on (possibly non reflexive) Banach spac...

Simons, Stephen

2008-01-01

271

Maximal regular boundary value problems in Banach-valued weighted space  

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Full Text Available This study focuses on nonlocal boundary value problems for elliptic ordinary and partial differential-operator equations of arbitrary order, defined in Banach-valued function spaces. The region considered here has a varying bound and depends on a certain parameter. Several conditions are obtained that guarantee the maximal regularity and Fredholmness, estimates for the resolvent, and the completeness of the root elements of differential operators generated by the corresponding boundary value problems in Banach-valued weighted spaces. These results are applied to nonlocal boundary value problems for regular elliptic partial differential equations and systems of anisotropic partial differential equations on cylindrical domain to obtain the algebraic conditions that guarantee the same properties.

Bohner Martin

2005-01-01

272

Maximal regular boundary value problems in Banach-valued weighted space  

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Full Text Available This study focuses on nonlocal boundary value problems for elliptic ordinary and partial differential-operator equations of arbitrary order, defined in Banach-valued function spaces. The region considered here has a varying bound and depends on a certain parameter. Several conditions are obtained that guarantee the maximal regularity and Fredholmness, estimates for the resolvent, and the completeness of the root elements of differential operators generated by the corresponding boundary value problems in Banach-valued weighted Lp spaces. These results are applied to nonlocal boundary value problems for regular elliptic partial differential equations and systems of anisotropic partial differential equations on cylindrical domain to obtain the algebraic conditions that guarantee the same properties.

Veli B. Shakhmurov

2005-02-01

273

Inexact NewtonLandweber iteration for solving nonlinear inverse problems in Banach spaces  

International Nuclear Information System (INIS)

By making use of duality mappings, we formulate an inexact NewtonLandweber iteration method for solving nonlinear inverse problems in Banach spaces. The method consists of two components: an outer Newton iteration and an inner scheme providing the increments by applying the Landweber iteration in Banach spaces to the local linearized equations. It has the advantage of reducing computational work by computing more cheap steps in each inner scheme. We first prove a convergence result for the exact data case. When the data are given approximately, we terminate the method by a discrepancy principle and obtain a weak convergence result. Finally, we test the method by reporting some numerical simulations concerning the sparsity recovery and the noisy data containing outliers. (paper)

2012-06-01

274

Some fixed point theorems for multivalued maps in ordered Banach spaces and applications  

Digital Repository Infrastructure Vision for European Research (DRIVER)

The existence of maximal and minimal fixed points for various set-valued operators is discussed. This paper presents some new fixed point theorems in ordered Banach spaces. A necessary and sufficient condition for the existence of the fixed point to a class of multivalued maps has been obtained. The uniqueness of the positive fixed point has been discussed. The results extend and improve the corresponding results. As an application, we utilize the results to study the existence and uniqueness...

2005-01-01

275

Hyers-Ulam stability of linear second-order differential equations in complex Banach spaces  

Directory of Open Access Journals (Sweden)

Full Text Available We prove the Hyers-Ulam stability of linear second-order differential equations in complex Banach spaces. That is, if y is an approximate solution of the differential equation $y''+ alpha y'(t +eta y = 0$ or $y''+ alpha y'(t +eta y = f(t$, then there exists an exact solution of the differential equation near to y.

Yongjin Li

2013-08-01

276

Application of He's homotopy perturbation method for a nonlinear functional equation in Banach spaces  

Science.gov (United States)

In the present paper we extend the Homotopy Perturbation Method to find an approximate analytic solution for a nonlinear functional equation in a Banach space. While previously necessary and sufficient conditions were given for the existence of the solution only for the case of a non expansive operator, HPM allowed us to find solutions also for the case of an expansive operator T, as shown in the given example.

Bota, C.; C?runtu, B.; Bund?u, O.

2013-10-01

277

Some Results for a Finite Family of Uniformly -Lipschitzian Mappings in Banach Spaces  

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Full Text Available The purpose of this paper is to prove a strong convergence theorem for a finite family of uniformly -Lipschitzian mappings in Banach spaces. The results presented in the paper not only correct some mistakes appeared in the paper by Ofoedu (2006 but also improve and extend some recent results by Chang (2001, Cho et al. (2005, Ofoedu (2006, Schu (1991, and Zeng (2003, 2005.

Chang Shih-Sen

2007-01-01

278

Some Results for a Finite Family of Uniformly L-Lipschitzian Mappings in Banach Spaces  

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Full Text Available The purpose of this paper is to prove a strong convergence theorem for a finite family of uniformly L-Lipschitzian mappings in Banach spaces. The results presented in the paper not only correct some mistakes appeared in the paper by Ofoedu (2006 but also improve and extend some recent results by Chang (2001, Cho et al. (2005, Ofoedu (2006, Schu (1991, and Zeng (2003, 2005.

Shih-Sen Chang

2007-07-01

279

Some Results for a Finite Family of Uniformly L-Lipschitzian Mappings in Banach Spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

The purpose of this paper is to prove a strong convergence theorem for a finite family of uniformly L-Lipschitzian mappings in Banach spaces. The results presented in the paper not only correct some mistakes appeared in the paper by Ofoedu (2006) but also improve and extend some recent results by Chang (2001), Cho et al. (2005), Ofoedu (2006), Schu (1991), and Zeng (2003, 2005).

Shih-Sen Chang; Jia Lin Huang; Xiong Rui Wang

2007-01-01

280

Iterations converging to distinct solutions of some nonlinear operator equations in Banach space  

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Full Text Available We examine the solvability of multilinear equations of the formMk(x,x,…,x−k   times−=y,   k=2,3,…where Mk is a k-linear operator on a Banach space X and y∈X is fixed.

Ioannis K. Argyros

1986-09-01

 
 
 
 
281

On some Banach space constants arising in nonlinear fixed point and eigenvalue theory  

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Full Text Available As is well known, in any infinite-dimensional Banach space one may find fixed point free self-maps of the unit ball, retractions of the unit ball onto its boundary, contractions of the unit sphere, and nonzero maps without positive eigenvalues and normalized eigenvectors. In this paper, we give upper and lower estimates, or even explicit formulas, for the minimal Lipschitz constant and measure of noncompactness of such maps.

Erzakova Nina A

2004-01-01

282

On some Banach space constants arising in nonlinear fixed point and eigenvalue theory  

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Full Text Available As is well known, in any infinite-dimensional Banach space one may find fixed point free self-maps of the unit ball, retractions of the unit ball onto its boundary, contractions of the unit sphere, and nonzero maps without positive eigenvalues and normalized eigenvectors. In this paper, we give upper and lower estimates, or even explicit formulas, for the minimal Lipschitz constant and measure of noncompactness of such maps.

Martin Vth

2004-12-01

283

Parametric general variational-like inequality problem in uniformly smooth Banach space  

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Full Text Available Using the concept of p-η-proximal mapping, we study the existence and sensitivity analysis of solution of a parametric general variational-like inequality problem in uniformly smooth Banach space. The approach used may be treated as an extension and unification of approaches for studying sensitivity analysis for various important classes of variational inequalities given by many authors in this direction.

F. A. Khan

2006-07-01

284

Fixed point iterations for strictly hemi-contractive maps in uniformly smooth Banach spaces  

International Nuclear Information System (INIS)

It is proved that the Mann iteration process converges strongly to the fixed point of a strictly hemi-contractive map in real uniformly smooth Banach spaces. The class of strictly hemi-contractive maps includes all strictly pseudo-contractive maps with nonempty fixed point sets. A related result deals with the Ishikawa iteration scheme when the mapping is Lipschitzian and strictly hemi-contractive. Our theorems generalize important known results. (author). 29 refs

1993-01-01

285

On the correct formulation of a nonlinear differential equations in Banach space  

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Full Text Available We study, the existence and uniqueness of the initial value problems in a Banach space E for the abstract nonlinear differential equation (dn−1/dtn−1(du/dt+Au=B(tu+f(t,W(t, and consider the correct solution of this problem. We also give an application of the theory of partial differential equations.

Fayez H. Michael

2001-05-01

286

Impulsive moving mirror model and impulsive differential equations in Banach space  

International Nuclear Information System (INIS)

The dependence of vacuum state energy on the distance between the uniformly relatively moving mirrors is used to calculate impulsive differential equations in Banach space. We formulate the problem of moving mirrors, possibly with suddenly change of velocity v in t=t_n, n=0, 1, 2, ..., upon which quantum fields satisfy Dirichlet boundary conditions, with the associated Casimir effect, in a functional Schroedinger picture. 10 refs

1992-01-01

287

Study of an Approximation Process of Time Optimal Control for Fractional Evolution Systems in Banach Spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Abstract The paper is devoted to the study of an approximation process of time optimal control for fractional evolution systems in Banach spaces. We firstly convert time optimal control problem into Meyer problem. By virtue of the properties of the family of solution operators given by us, the existence of optimal controls for Meyer problem is proved. Secondly, we construct a sequence of Meyer problems to successive approximation of the original time optimal control problem. Finally...

2011-01-01

288

A New Strong Convergence Theorem for Equilibrium Problems and Fixed Point Problems in Banach Spaces  

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Full Text Available We introduce a new iterative sequence for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of an equilibrium problem in a Banach space. Then, we study the strong convergence of the sequences. With an appropriate setting, we obtain the corresponding results due to Takahashi-Takahashi and Takahashi-Zembayashi. Some of our results are established with weaker assumptions.

Nilsrakoo Weerayuth

2011-01-01

289

Iterations converging to distinct solutions of some nonlinear operator equations in Banach space  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We examine the solvability of multilinear equations of the formMk(x,x,…,x)−k   times−=y,   k=2,3,…where Mk is a k-linear operator on a Banach space X and y∈X is fixed.

1986-01-01

290

Uniform exponential stability of linear periodic systems in a Banach space  

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Full Text Available This article is devoted to the study of linear periodic dynamical systems, possessing the property of uniform exponential stability. It is proved that if the Cauchy operator of these systems possesses a certain compactness property, then the asymptotic stability implies the uniform exponential stability. We also show applications to different classes of linear evolution equations, such as ordinary linear differential equations in the space of Banach, retarded and neutral functional differential equations, some classes of evolution partial differential equations.

David N. Cheban

2001-01-01

291

Existence of weak and strong solutions of nonlinear differential equations with delay in Banach space  

Energy Technology Data Exchange (ETDEWEB)

Existence of weak and strong solutions of nonlinear differential equations with delay in Banach space is discussed. In the present work we give a generalization to recent results. We prove that, with certain conditions, every nonlinear differential equation with delay has at least one weak solution, furthermore, under suitable assumptions, these equations have solutions. Next under a generalization of the compactness assumptions, we show the same equations have solutions too.

Gomaa, A M [Department of Mathematics, Faculty of Science, Helwan University (Egypt)], E-mail: gomaa5@hotmail.com

2008-02-15

292

The initial value problem for the heat convection equations with the dissipation in Banach spaces  

CERN Multimedia

We consider the abstract initial value problem for evolution equations which describe heat convection of incompressible viscous fluids. It is difficulty that we do not neglect the dissipation function in contrast to the Boussinesq approximation. This problem has uniquely a mild solution. Moreover, a mild solution of this problem can be a strong or classical solution under appropriate assumptions for initial data. We prove the above properties by the theory of analytic semigroups on Banach spaces.

Kakizawa, Ryhei

2009-01-01

293

Robustness of a nonuniform (mu,nu trichotomy in Banach spaces  

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Full Text Available In this article, we consider the robustness of a nonuniform $(mu,u$ trichotomy in Banach spaces, in the sense that the existence of such a trichotomy for a given linear equation persists under sufficiently small linear perturbations. The continuous dependence with the perturbation of the constants in the notion of trichotomy is studied, and the related robustness of strong $(mu,u$ trichotomy is also presented.

Yongxin Jiang

2012-09-01

294

ISOMETRIC WEIGHTED COMPOSITION OPERATORS ON WEIGHTED BANACH SPACES OF HOLOMORPHIC FUNCTIONS DEFINED ON THE UNIT BALL OF A COMPLEX BANACH SPACE  

Scientific Electronic Library Online (English)

Full Text Available SciELO Chile | Language: English Abstract in spanish Sea X y Y espacios de Banach complejos, B X y B Y las bolas unitarias cerradas correspondientes. Las aplicaciones analticas : B Y [...] width=29 height=24 id="_x0000_i1044" src="http:/fbpe/img/cubo/v15n2/art04-02.jpg" alt="Descripcin: http:/fbpe/img/cubo/v15n2/art04-02.jpg">B X y: B X inducen el operador de composicin con pesos: C , : H (B Y) H (Bx), f (f o ), donde H (B Y) y H (Bx) denotan la coleccin de todas las funciones analticas f : Bx (resp. B Y) . Estudiamos cundo dichos operadores que actan entre los espacios con peso de funciones analticas son isomtricas. Abstract in english Let X and Y be complex Banach spaces and B X resp. B Y the closed unit ball. Analytic maps : B Y [...] " src="http:/fbpe/img/cubo/v15n2/art04-02.jpg" alt="Descripcin: http:/fbpe/img/cubo/v15n2/art04-02.jpg">B X and : B X induce the weighted composition operator: C , : H (B Y) H (Bx), f (f o ), where H (B Y) resp. H (Bx) denotes the collection of all analytic functions f : Bx (resp. B Y) . We study when such operators acting between weighted spaces of analytic functions are isometric.

Wolf, Elke.

295

Property $(M)$, $M$-ideals, and almost isometric structure of Banach spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We study $M$-ideals of compact operators by means of the property~$(M)$ introduced in \\cite{Kal-M}. Our main result states for a separable Banach space $X$ that the space of compact operators on $X$ is an $M$-ideal in the space of bounded operators if (and only if) $X$ does not contain a copy of $\\ell_{1}$, has the metric compact approximation property, and has property~$(M)$. The investigation of special versions of property~$(M)$ leads to results on almost isometric struct...

Kalton, Nigel J.; Werner, Dirk

1993-01-01

296

Reflexive Numbers and Berger Graphs from Calabi-Yau Spaces  

CERN Document Server

A novel relation between number theory and recently found Berger graphs is studied. The Berger graphs under investigation are constructed mainly for the CY_3 space. The method of analysis is based on the slice classification of CY_l polyhedra in the so-called Universal Calabi-Yau algebra. The concept of reflexivity in these polyhedra is reviewed and translated into the theory of reflexive numbers. A new approach based on recurrence relations and Quantum Field Theory methods is applied to the simply-laced and quasi-simply-laced subsets of the reflexive numbers. In the correspondence between the reflexive vectors and Berger graphs the role played by the generalized Coxeter labels is shown to be important. We investigate the positive roots of some of the Berger graphs to guess the algebraic structure hidden behind them.

Lipatov, L N; Velizhanin, V N; Volkov, G G

2006-01-01

297

Some Geometric Inequalities in a New Banach Sequence Space  

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Full Text Available The difference sequence space , which is a generalization of the space introduced and studied by Sargent (1960, was defined by olak and Et (2005. In this paper we establish some geometric inequalities for this space.

olak Rifat

2007-01-01

298

Hilbert space frames containing a Riesz basis and Banach spaces which have no subspace isomorphic to $c_0$  

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We prove that a Hilbert space frame $\\fti$ contains a Riesz basis if every subfamily $\\ftj , J \\subseteq I ,$ is a frame for its closed span. Secondly we give a new characterization of Banach spaces which do not have any subspace isomorphic to $c_0$. This result immediately leads to an improvement of a recent theorem of Holub concerning frames consisting of a Riesz basis plus finitely many elements.

Casazza, Peter G.; Christensen, Ole

1995-01-01

299

Hilbert space frames containing a Riesz basis and Banach spaces which have no subspace isomorphic to $c_{0}$  

CERN Document Server

We prove that a Hilbert space frame $\\fti$ contains a Riesz basis if every subfamily $\\ftj , J \\subseteq I ,$ is a frame for its closed span. Secondly we give a new characterization of Banach spaces which do not have any subspace isomorphic to $c_0$. This result immediately leads to an improvement of a recent theorem of Holub concerning frames consisting of a Riesz basis plus finitely many elements.

Casazza, P G; Casazza, Peter G.; Christensen, Ole

1995-01-01

300

A type (4) space in (FR)-classification  

CERN Document Server

We present a reflexive Banach space with an unconditional basis which is quasi-minimal and tight by range, i.e. of type (4) in Ferenczi-Rosendal list within the framework of Gowers' classification program of Banach spaces. The space is an unconditional variant of the Gowers Hereditarily Indecomposable space with asymptotically unconditional basis.

Argyros, Spiros A; Pelczar-Barwacz, Anna

2012-01-01

 
 
 
 
301

Some Geometric Inequalities in a New Banach Sequence Space  

Directory of Open Access Journals (Sweden)

Full Text Available The difference sequence space m(φ,p,Δ(r, which is a generalization of the space m(φ introduced and studied by Sargent (1960, was defined by Çolak and Et (2005. In this paper we establish some geometric inequalities for this space.

Mikail Et

2007-12-01

302

Some Geometric Inequalities in a New Banach Sequence Space  

Digital Repository Infrastructure Vision for European Research (DRIVER)

The difference sequence space m(φ,p,Δ(r)), which is a generalization of the space m(φ) introduced and studied by Sargent (1960), was defined by Çolak and Et (2005). In this paper we establish some geometric inequalities for this space.

Mursaleen, M.; Rifat olak; Mikail Et

2007-01-01

303

On positive solutions of functional-differential equations in banach spaces  

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Full Text Available In this paper, we deal with two point boundary value problem (BVP for the functional-differential equation of second order where the function takes values in a cone of a Banach space . For and we obtain the BVP with reflection of the argument. Applying fixed point theorem on strict set-contraction from G. Li, Proc. Amer. Math. Soc. 97 (1986, 277280, we prove the existence of positive solution in the space . Some inequalities involving and the respective Green's function are used. We also give the application of our existence results to the infinite system of functionaldifferential equations in the case .

Zima Miros?awa

2001-01-01

304

Existence and uniqueness of solutions for fourth-order boundary-value problems in Banach spaces  

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Full Text Available This article concerns the fourth-order boundary-value problem $$displaylines{ x^{(4}(t=f(t,x(t,x''(t,quad tin (0,1,cr x(0=x(1=x''(0=x''(1=heta, }$$ in a Banach space. We present some spectral conditions, on the nonlinearity $f(t,u,v$, to guarantee the existence and uniqueness of solutions. Our method is different from the one used in the references, even the above problem in a scalar space.

2009-02-01

305

Stochastic Volterra Equations in Banach Spaces and Stochastic Partial Differential Equations  

CERN Document Server

In this paper, we first study the existence-uniqueness and large deviation estimate of solutions for stochastic Volterra integral equations with singular kernels in 2-smooth Banach spaces. Then, we apply them to a large class of semilinear stochastic partial differential equations (SPDE) driven by Brownian motions as well as by fractional Brownian motions, and obtain the existence of unique maximal strong solutions (in the sense of SDE and PDE) under local Lipschitz conditions. Lastly, high order SPDEs in a bounded domain of Euclidean space, second order SPDEs on complete Riemannian manifolds, as well as stochastic Navier-Stokes equations are investigated.

Zhang, Xicheng

2008-01-01

306

Weak Convergence and Banach Space-Valued Functions: Improving the Stability Theory of Feynman's Operational Calculi  

Science.gov (United States)

In this paper we investigate the relation between weak convergence of a sequence left\\{ ?nright\\} of probability measures on a Polish space S converging weakly to the probability measure ? and continuous, norm-bounded functions into a Banach space X. We show that, given a norm-bounded continuous function f: S? X, it follows that lim_{ntoinfty}intSf d?n=intSf d?the limit one has for bounded and continuous real (or complex)valued functions on S. This result is then applied to the stability theory of Feynman's operational calculus where it is shown that the theory can be significantly improved over previous results.

Nielsen, Lance

2011-12-01

307

Weak Convergence Theorems for a Countable Family of Strict Pseudocontractions in Banach Spaces  

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Full Text Available We investigate the convergence of Mann-type iterative scheme for a countable family of strict pseudocontractions in a uniformly convex Banach space with the Frchet differentiable norm. Our results improve and extend the results obtained by Marino-Xu, Zhou, Osilike-Udomene, Zhang-Guo and the corresponding results. We also point out that the condition given by Chidume-Shahzad (2010 is not satisfied in a real Hilbert space. We show that their results still are true under a new condition.

Cholamjiak Prasit

2010-01-01

308

The Aron-Berner extension for polynomials defined in the dual of a Banach space  

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Let E = F' where F is a complex Banach space and let pi(1) : E" - E circle plus F-perpendicular to --> E be the canonical projection. Let P(E-n) be the space of the complex valued continuous n-homogeneous polynomials defined in E. We characterize the elements P is an element of P(E-n) whose Aron-Berner extension coincides with P circle pi(1). The case of weakly continuous polynomials is considered. Finally we also study the same problem for holomorphic functions of bounded type.

Llavona, Jose? G.; Moraes, Luiza A.

2004-01-01

309

Convergence rates for the iteratively regularized GaussNewton method in Banach spaces  

International Nuclear Information System (INIS)

In this paper we consider the iteratively regularized GaussNewton method (IRGNM) in a Banach space setting and prove optimal convergence rates under approximate source conditions. These are related to the classical concept of source conditions that is available only in Hilbert space. We provide results in the framework of general index functions, which include, e.g. Hlder and logarithmic rates. Concerning the regularization parameters in each Newton step as well as the stopping index, we provide both a priori and a posteriori strategies, the latter being based on the discrepancy principle

2010-03-01

310

The Natural Banach Space for Version Independent Risk Measures  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Risk measures, or coherent measures of risk are often considered on the space $L^\\infty$, and important theorems on risk measures build on that space. Other risk measures, among them the most important risk measure the Average Value-at-Risk are well-defined on the larger space $L^1$ and this seems to be the natural domain space for this risk measure. Spectral risk measures constitute a further class of risk measures of central importance, and they are often considered on some $L^...

Pichler, Alois

2013-01-01

311

Double-dual n-types over Banach spaces not containing ℓ1  

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Full Text Available Let E be a Banach space. The concept of n-type overE is introduced here, generalizing the concept of type overE introduced by Krivine and Maurey. Let E″ be the second dual of E and fix g″1,…g″n∈E″. The function τ:E×ℝn→ℝ, defined by letting τ(x,a1,…,an=‖x+∑i=1naig″i‖ for all x∈E and all a1,…,an∈ℝ, defines an n-type over E. Types that can be represented in this way are called double-dual n-types; we say that (g″1,…g″n∈(E″n realizes τ. Let E be a (not necessarily separable Banach space that does not contain ℓ1. We study the set of elements of (E″n that realize a given double-dual n-type over E. We show that the set of realizations of this n-type is convex. This generalizes a result of Haydon and Maurey who showed that the set of realizations of a given 1-type over a separable Banach space E is convex. The proof makes use of Henson's language for normed space structures and uses ideas from mathematical logic, most notably the Löwenheim-Skolem theorem.

Markus Pomper

2004-07-01

312

Asymptotic geometry of Banach spaces and non linear quotients.  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Recently, Lima and Randrianarivony pointed out the role of the property (beta ) of Rolewicz in nonlinear quotient problems, and answered a ten-year-old question of Bates, Johnson, Lindenstrauss, Preiss and Schechtman. In the present paper, we prove that the modulus of asymptotic uniform smoothness of the range space of a uniform quotient map can be compared with the modulus of (beta ) of the domain space. We also provide conditions under which this comparison can be improved.

2013-01-01

313

Approximating Common Fixed Points of Lipschitzian Semigroup in Smooth Banach Spaces  

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Full Text Available Abstract Let be a left amenable semigroup, let be a representation of as Lipschitzian mappings from a nonempty compact convex subset of a smooth Banach space into with a uniform Lipschitzian condition, let be a strongly left regular sequence of means defined on an -stable subspace of , let be a contraction on , and let , , and be sequences in (0, 1 such that , for all . Let , for all . Then, under suitable hypotheses on the constants, we show that converges strongly to some in , the set of common fixed points of , which is the unique solution of the variational inequality , for all .

Saeidi Shahram

2008-01-01

314

Modulus of Convexity, the Coeffcient R(1,X, and Normal Structure in Banach Spaces  

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Full Text Available Let δX(ϵ and R(1,X be the modulus of convexity and the Domínguez-Benavides coefficient, respectively. According to these two geometric parameters, we obtain a sufficient condition for normal structure, that is, a Banach space X has normal structure if 2δX(1+ϵ>max{(R(1,x-1ϵ,1-(1-ϵ/R(1,X-1} for some ϵ∈[0,1] which generalizes the known result by Gao and Prus.

Fenghui Wang

2008-06-01

315

Perturbed Iterative Approximation of Solutions for Nonlinear General -Monotone Operator Equations in Banach Spaces  

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Full Text Available We introduce and study a new class of nonlinear general -monotone operator equations with multivalued operator. By using Alber's inequalities, Nalder's results, and the new proximal mapping technique, we construct some new perturbed iterative algorithms with mixed errors for solving the nonlinear general -monotone operator equations and study the approximation-solvability of the nonlinear operator equations in Banach spaces. The results presented in this paper improve and generalize the corresponding results on strongly monotone quasivariational inclusions and nonlinear implicit quasivariational inclusions.

Lan Heng-you

2009-01-01

316

Approximation of fixed points of Lipschitz pseudo-contractive mapping in Banach spaces  

International Nuclear Information System (INIS)

Let K be a subset of a real Banach space X. A mapping T:K ? X is called pseudo-contractive if the inequality ||x-y|| ? ||(1+r)(x-y)-r(Tx-Ty)|| holds for all x,y in K and r > 0. Fixed points of Lipschitz pseudo-contractive maps are approximated under appropriate conditions, by an iteration process of the type introduced by W.R. Mann. This gives an affirmative answer to the problem stated by T.L. Hicks and J.R. Rubicek (J. Math. Anal. Appl. 59 (1977) 504). (author). 28 refs

1988-01-01

317

Study of an Approximation Process of Time Optimal Control for Fractional Evolution Systems in Banach Spaces  

Directory of Open Access Journals (Sweden)

Full Text Available Abstract The paper is devoted to the study of an approximation process of time optimal control for fractional evolution systems in Banach spaces. We firstly convert time optimal control problem into Meyer problem. By virtue of the properties of the family of solution operators given by us, the existence of optimal controls for Meyer problem is proved. Secondly, we construct a sequence of Meyer problems to successive approximation of the original time optimal control problem. Finally, a new approximation process is established to find the solution of time optimal control problem. Our method is different from the standard method.

Zhou Yong

2011-01-01

318

Perturbation of strong Feller semigroups and well-posedness of semilinear stochastic equations on Banach spaces  

CERN Document Server

We prove a Miyadera-Voigt type perturbation theorem for strong Feller semigroups. Using this result, we prove well-posedness of the semilinear stochastic equation dX(t) = [AX(t) + F(X(t))]dt + GdW_H(t) on a separable Banach space E, assuming that F is bounded and measurable and that the associated linear equation, i.e.\\ the equation with F = 0, is well-posed and its transition semigroup is strongly Feller and satisfies an appropriate gradient estimate. We also study existence and uniqueness of invariant measures for the associated transition semigroup and discuss extensions of our results to nonlinearities F which are unbounded.

Kunze, Markus C

2011-01-01

319

Some fixed point theorems for multivalued maps in ordered Banach spaces and applications  

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Full Text Available The existence of maximal and minimal fixed points for various set-valued operators is discussed. This paper presents some new fixed point theorems in ordered Banach spaces. A necessary and sufficient condition for the existence of the fixed point to a class of multivalued maps has been obtained. The uniqueness of the positive fixed point has been discussed. The results extend and improve the corresponding results. As an application, we utilize the results to study the existence and uniqueness of positive fixed points for a class of convex operators. In the end, we give a simple application to certain integral equations.

Zhai Chengbo

2005-12-01

320

Banach SSD spaces and classes of monotone sets  

CERN Document Server

In this paper, we unify the theory of SSD spaces and the theory of strongly representable sets, and we apply our results to the theory of the various classes of maximally monotone sets. In particular, we prove that type (ED), dense type, type (D) and type (NI) are identical.

Simons, Stephen

2009-01-01

 
 
 
 
321

Good Banach spaces for piecewise hyperbolic maps via interpolation  

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We introduce a weak transversality condition for piecewise C^{1+\\alpha} and piecewise hyperbolic maps which admit a C^{1+\\alpha} stable distribution. We show good bounds on the essential spectral radius of the associated transfer operators acting on classical anisotropic Sobolev spaces of Triebel-Lizorkin type. In many cases, we obtain a spectral gap from which we deduce the existence of finitely many physical measures with basin of total measure. The analysis relies on stan...

Baladi, Viviane; Gouezel, Sebastien

2007-01-01

322

Strong Convergence Theorems of Viscosity Iterative Methods for a Countable Family of Strict Pseudo-contractions in Banach Spaces  

Directory of Open Access Journals (Sweden)

Full Text Available For a countable family of strictly pseudo-contractions, a strong convergence of viscosity iteration is shown in order to find a common fixed point of in either a p-uniformly convex Banach space which admits a weakly continuous duality mapping or a p-uniformly convex Banach space with uniformly Gteaux differentiable norm. As applications, at the end of the paper we apply our results to the problem of finding a zero of accretive operators. The main result extends various results existing in the current literature.

Wangkeeree Rabian

2010-01-01

323

Cauchy-Stieltjes integral on time scales in banach spaces and hysteresis operators  

Science.gov (United States)

The play operator has a fundamental importance in the theory of hysteresis. It was studied in various settings as shown by P. Krejci and Ph. Laurenot in 2002. In that work it was considered the Young integral in the frame of Hilbert spaces. Here we study the play in the frame of the regulated functions (that is: the ones having only discontinuities of the first kind) on a general time scale T (that is: with T being a nonempty closed set of real numbers) with values in a Banach space. We will be showing that the dual space in this case will be defined as the space of operators of bounded semivariation if we consider as the bilinearity pairing the Cauchy-Stieltjes integral on time scales.

Barbanti, Luciano; Damasceno, Berenice Camargo

2012-11-01

324

Impulsive moving mirror model in a Schroedinger picture with impulse effect in a Banach space  

International Nuclear Information System (INIS)

From a special class of systems has been used a Schroedinger equation with impulse effect in Minkowski space field theory with time dependent boundary conditions, i.e. those of moving mirrors. The field theoretical approach for studing the properties of the vacuum starts from an analysis of the behaviour of local field quantities in Minkowski space with uniformly moving mirrors. For the impulsive moving mirror model is the real process of interaction between the quantum field and the external mirror a subject to disturbances in its evolution acting in time very short compared with the entire duration of the process. So the stability of the solution of the Schroedinger evolution equation for the process is the stability of the vacuum of Casimir. The dependence of vacuum state energy on the distance between the uniformly relatively moving mirrors is used to calculate from the impulsive moving model the Schroedinger equation in a Banach space. 21 refs

1992-01-01

325

Existence of mild solutions of second-order neutral functional differential inclusions with nonlocal conditions in Banach spaces  

Directory of Open Access Journals (Sweden)

Full Text Available We study the existence of mild solutions of the nonlinear second-order neutral functional differential and integrodifferential inclusions with nonlocal conditions in Banach spaces. The results are obtained by using the theory of strongly continuous cosine families of bounded linear operators and a fixed point theorem for condensing maps due to Martelli.

J. P. Dauer

2004-05-01

326

Strong Convergence of an Implicit Iteration Process for a Finite Family of Uniformly -Lipschitzian Mappings in Banach Spaces  

Directory of Open Access Journals (Sweden)

Full Text Available The purpose of this paper is to prove a strong convergence theorem for a finite family of uniformly -Lipschitzian mappings in Banach spaces. The results presented in the paper improve and extend the corresponding results announced by Chang (2001, Cho et al. (2005, Ofoedu (2006, Schu (1991 and Zeng (2003 and 2005, and many others.

Gu Feng

2010-01-01

327

Strong Convergence of an Implicit Iteration Process for a Finite Family of Uniformly L-Lipschitzian Mappings in Banach Spaces  

Directory of Open Access Journals (Sweden)

Full Text Available The purpose of this paper is to prove a strong convergence theorem for a finite family of uniformly L-Lipschitzian mappings in Banach spaces. The results presented in the paper improve and extend the corresponding results announced by Chang (2001, Cho et al. (2005, Ofoedu (2006, Schu (1991 and Zeng (2003 and 2005, and many others.

Feng Gu

2010-01-01

328

Strong Convergence of an Implicit Iteration Process for a Finite Family of Uniformly L-Lipschitzian Mappings in Banach Spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

The purpose of this paper is to prove a strong convergence theorem for a finite family of uniformly L-Lipschitzian mappings in Banach spaces. The results presented in the paper improve and extend the corresponding results announced by Chang (2001), Cho et al. (2005), Ofoedu (2006), Schu (1991) and Zeng (2003 and 2005), and many others.

Feng Gu

2010-01-01

329

Weak and Strong Convergence of an Implicit Iteration Process for an Asymptotically Quasi- -Nonexpansive Mapping in Banach Space  

Directory of Open Access Journals (Sweden)

Full Text Available We prove the weak and strong convergence of the implicit iterative process to a common fixed point of an asymptotically quasi- -nonexpansive mapping and an asymptotically quasi-nonexpansive mapping , defined on a nonempty closed convex subset of a Banach space.

Mukhamedov Farrukh

2010-01-01

330

Regularization proximal point algorithm for finding a common fixed point of a finite family of nonexpansive mappings in Banach spaces  

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Full Text Available Abstract We study the strong convergence of a regularization proximal point algorithm for finding a common fixed point of a finite family of nonexpansive mappings in a uniformly convex and uniformly smooth Banach space. 2010 Mathematics Subject Classification: 47H09; 47J25; 47J30.

Tuyen Truong

2011-01-01

331

Weak and Strong Convergence of an Implicit Iteration Process for an Asymptotically Quasi-I-Nonexpansive Mapping in Banach Space  

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Full Text Available We prove the weak and strong convergence of the implicit iterative process to a common fixed point of an asymptotically quasi-I-nonexpansive mapping T and an asymptotically quasi-nonexpansive mapping I, defined on a nonempty closed convex subset of a Banach space.

Farrukh Mukhamedov

2010-01-01

332

Positive solutions for a high-order multi-point boundary-value problem in Banach spaces  

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Full Text Available Using the fixed point theory of strict set contractions, we study the existence of at least one, two, and multiple positive solutions for higher order multiple point boundary-value problems in Banach spaces. Our result extends some of the existing results.

Weihua Jiang

2008-05-01

333

Positive solutions for second-order multi-point boundary-value problems at resonance in Banach spaces  

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Full Text Available In this article, we study the existence and multiplicity of positive solutions for a nonlinear second-order multi-point boundary-value problem at resonance in Banach spaces. The arguments are based upon a specially constructed equivalent equation and the fixed point theory in a cone for strict set contraction operators.

Weihua Jiang

2011-02-01

334

A unified approach for constructing fast two-step methods in Banach space and their applications  

Energy Technology Data Exchange (ETDEWEB)

We introduce some new very general ways of constructing fast two-step methods to approximate a locally unique solution of a nonlinear operator equation in a Banach space setting. We provide existence-uniqueness theorems as well as an error analysis for the iterations involved using Newton-Kantorovich-type hypotheses and the majorant method. Our results depend on the existence of a Lipschitz function defined on a closed ball centered at a certain point and of a fixed radius and with values into the positive real axis. Special choices of this function lead to favorable comparisons with results already in the literature. The monotone convergence is also examined in a partially ordered topological space setting. Some applications to the solution of nonlinear integral equations appearing in radiative transfer as well as to the solution of integral equations of Uryson-type are also provided.

Argyros, I.K. [Cameron Univ., Lawton, OK (United States)

1996-12-31

335

Pathwise uniqueness for stochastic reaction-diffusion equations in Banach spaces with an H\\"{o}lder drift component  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We prove pathwise uniqueness for an abstract stochastic reaction-diffusion equation in Banach spaces. The drift contains a bounded H\\"{o}lder term; in spite of this, due to the space-time white noise it is possible to prove pathwise uniqueness. The proof is based on a detailed analysis of the associated Kolmogorov equation. The model includes examples not covered by the previous works based on Hilbert spaces or concrete SPDEs.

Cerrai, Sandra; Da Prato, Giuseppe; Flandoli, Franco

2012-01-01

336

Convergence of hybrid steepest descent method for variational inequalities in Banach spaces  

International Nuclear Information System (INIS)

Let E be a real q-uniformly smooth Banach space with constant dq, q ? 2. Let T : E ? E and G : E ? E be a nonexpansive map and an ?-strongly accretive map which is also ? - Lipschitzian, respectively. Let {?n} be a real sequence in [0, 1] satisfying some appropriate conditions. For ? element of (0, ( q ?/dq ?q )q-1 ), define a sequence { xn} iteratively in E by x0 element of E, xn+1 = T?n+1 xn = Txn - ? ?n+1 G(Txn), n ? 0. Then, {xn} converges strongly to the unique solution x* of the variational inequality problem VI(G,K) (search for x* element of K such that q(y - x*)> ? 0 for all y element of K), where K := Fix(T) { x element of E : Tx = x} ? 0. A convergence theorem related to fi nite family of nonexpansive maps is also proved. (author)

2007-01-01

337

Picard iterations for nonlinear Lipschitz strong pseudo-contractions in uniformly smooth Banach spaces  

International Nuclear Information System (INIS)

Suppose E is a real uniformly smooth Banach space and K is a nonempty closed convex and bounded subset of E, T:K ? K is a Lipschitz pseudo-contraction. It is proved that the Picard iterates of a suitably defined operator converges strongly to the unique fixed point of T. Furthermore, this result also holds for the slightly larger class of Lipschitz strong hemi-contractions. Related results deal with strong convergence of the Picard iterates to the unique solution of operator equations involving Lipschitz strongly accretive maps. Apart from establishing strong convergence, our theorems give existence, uniqueness and convergence-rate which is at least as fast as a geometric progression. (author). 51 refs

1995-01-01

338

Linear Impulsive Periodic System with Time-Varying Generating Operators on Banach Space  

Directory of Open Access Journals (Sweden)

Full Text Available A class of the linear impulsive periodic system with time-varying generating operators on Banach space is considered. By constructing the impulsive evolution operator, the existence of T0-periodic PC-mild solution for homogeneous linear impulsive periodic system with time-varying generating operators is reduced to the existence of fixed point for a suitable operator. Further the alternative results on T0-periodic PC-mild solution for nonhomogeneous linear impulsive periodic system with time-varying generating operators are established and the relationship between the boundness of solution and the existence of T0-periodic PC-mild solution is shown. The impulsive periodic motion controllers that are robust to parameter drift are designed for a given periodic motion. An example given for demonstration.

JinRong Wang

2007-10-01

339

Strong convergence theorem for two asymptotically quasi-nonexpansive mappings with errors in Banach space  

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Full Text Available In this paper, we study strong convergence of common fixed points of two asymptotically quasi-nonexpansive mappings and prove that if $K$ is a nonempty closed convex subset of a real Banach space $E$ and let $ S, T\\colon K\\to K $ be two asymptotically quasi-nonexpansive mappings with sequences $ \\{u_n\\}$, $\\{v_n\\}\\subset [0,\\infty $ such that $ \\sum_{n=1}^{\\infty}u_n$$ \\begin{cases} x_{n+1}& = (1-\\alpha_nx_n + \\alpha_nS^ny_n + l_n \\\\ y_n &= (1-\\beta_nx_n + \\beta_nT^nx_n + m_n, \\quad \\forall n\\in N \\end{cases} $$where $ \\{l_n\\}_{n=1}^{\\infty},\\{m_n\\}_{n=1}^{\\infty} $ are sequences in $K$ satisfying $ \\sum_{n=1}^{\\infty}\\Vert l_n\\Vert

G. S. Saluja

2007-03-01

340

Asymptotic expansions for the Laplace approximations of sums of Banach space-valued random variables  

CERN Document Server

Let X_i, i\\in N, be i.i.d. B-valued random variables, where B is a real separable Banach space. Let \\Phi be a smooth enough mapping from B into R. An asymptotic evaluation of Z_n=E(\\exp (n\\Phi (\\sum_{i=1}^nX_i/n))), up to a factor (1+o(1)), has been gotten in Bolthausen [Probab. Theory Related Fields 72 (1986) 305-318] and Kusuoka and Liang [Probab. Theory Related Fields 116 (2000) 221-238]. In this paper, a detailed asymptotic expansion of Z_n as n\\to \\infty is given, valid to all orders, and with control on remainders. The results are new even in finite dimensions.

Albeverio, S; Albeverio, Sergio; Liang, Song

2005-01-01

 
 
 
 
341

Linear Impulsive Periodic System with Time-Varying Generating Operators on Banach Space  

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Full Text Available A class of the linear impulsive periodic system with time-varying generating operators on Banach space is considered. By constructing the impulsive evolution operator, the existence of -periodic -mild solution for homogeneous linear impulsive periodic system with time-varying generating operators is reduced to the existence of fixed point for a suitable operator. Further the alternative results on -periodic -mild solution for nonhomogeneous linear impulsive periodic system with time-varying generating operators are established and the relationship between the boundness of solution and the existence of -periodic -mild solution is shown. The impulsive periodic motion controllers that are robust to parameter drift are designed for a given periodic motion. An example given for demonstration.

Wei W

2007-01-01

342

On the Banach Problem on Surjections  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Is shown that any separable superreflexive Banach space X may be isometrically embedded in a separable superreflexive Banach space Z=Z(X) (which, in addition, is of the same type and cotype as X) such that its conjugate admits a continuous surjection on each its subspace. This gives an affirmative answer on S. Banach problem: Whether there exists a Banach space X, non isomorphic to a Hilbert space, which admits a continuous linear surjection on each its subspace and is essen...

Tokarev, Eugene

2002-01-01

343

Some estimates for the Banach space norms in the von Neumann algebras associated with the Berezin's quantization of compact Riemann  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Let $\\G$ be any cocompact, discrete subgroup of $\\pslr$. In this paper we find estimates for the predual and the uniform Banach space norms in the von Neumann algebras associated with the Berezin' s quantization of a compact Riemann surface $\\Bbb D/\\G$. As a corollary, for large values of the deformation parameter $1/h$, these von Neumann algebras are isomorphic. Using the results in [AS], [AC], [GHJ] on the von Neumann dimension of the Hilbert spaces in the discrete series ...

Radulescu, Florin

1995-01-01

344

Quasi-geostrophic equations with initial data in Banach spaces of local measures  

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Full Text Available This paper studies the well posedness of the initial value problem for the quasi-geostrophic type equations $$displaylines{ partial_{t}heta+u ablaheta+( -Delta ^{gamma}heta =0 quad hbox{on }mathbb{R}^{d}imes] 0,+infty[cr heta( x,0 =heta_{0}(x, quad xinmathbb{R}^{d} }$$ where 0 less than $gammaleq 1$ is a fixed parameter and the velocity field $u=(u_{1},u_{2},dots,u_{d} $ is divergence free; i.e., $ abla u=0$. The initial data $heta_{0}$ is taken in Banach spaces of local measures (see text for the definition, such as Multipliers, Lorentz and Morrey-Campanato spaces. We will focus on the subcritical case 1/2 less than $gammaleq1$ and we analyse the well-posedness of the system in three basic spaces: $L^{d/r,infty}$, $dot {X}_{r}$ and $dot {M}^{p,d/r}$, when the solution is global for sufficiently small initial data. Furtheremore, we prove that the solution is actually smooth. Mild solutions are obtained in several spaces with the right homogeneity to allow the existence of self-similar solutions.

Sadek Gala

2005-06-01

345

ON THE LOCAL CONVERGENCE OF A MIDPOINT METHOD IN BANACH SPACES UNDER A GAMMA-TYPE CONDITION  

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Full Text Available In this study we are concerned with the problem of approximating a locally unique solution of an operator equation in a Banach space setting using the midpoint method, introduced by us in [5], [6]. Here, we use gamma-type condition to provide a local convergence analysis. Our results compare favorably with the relevant ones in [9], [11], [12]-[14]- In particular our radius of convergence is larger. Numerical examples are also provided.

Ioannis K Argyros

2009-08-01

346

A Class of Semilocal E-Preinvex Maps in Banach Spaces with Applications to Nondifferentiable Vector Optimization  

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Full Text Available In this paper, a new class of semilocal E-preinvex and related maps in Banach spaces is introduced for a nondi?erentiable vector optimization problem with restrictions of inequalities and some of its basic properties are studied. Furthermore, as its applications, some optimality conditions and duality results are established for a nondi?erentiable vector optimization under the aforesaid maps assumptions.

Hehua Jiao

2014-01-01

347

A $c\\_0$-saturated Banach space with no long unconditional basic sequences  

CERN Document Server

We present a Banach space $\\mathfrak X$ with a Schauder basis of length $\\omega\\_1$ which is saturated by copies of $c\\_0$ and such that for every closed decomposition of a closed subspace $X=X\\_0\\oplus X\\_1$, either $X\\_0$ or $X\\_1$ has to be separable. This can be considered as the non-separable counterpart of the notion of hereditarily indecomposable space. Indeed, the subspaces of $\\mathfrak X$ have ``few operators'' in the sense that every bounded operator $T:X \\to \\mathfrak{X}$ from a subspace $X$ of $\\mathfrak{X}$ into $\\mathfrak{X}$ is the sum of a multiple of the inclusion and a $\\omega\\_1$-singular operator, i.e., an operator $S$ which is not an isomorphism on any non-separable subspace of $X$. We also show that while $\\mathfrak{X}$ is not distortable (being $c\\_0$-saturated), it is arbitrarily $\\omega\\_1$-distortable in the sense that for every $\\lambda>1$ there is an equivalent norm $\\||\\cdot \\||$ on $\\mathfrak{X}$ such that for every non-separable subspace $X$ of $\\mathfrak{X}$ there are $x,y\\in ...

Abad, J J; Abad, Jordi Lopez; Todorcevic, Stevo

2006-01-01

348

Quadratic equations in Banach space, perturbation techniques and applications to Chandrasekhar's and related equations  

International Nuclear Information System (INIS)

In this dissertation perturbation techniques are developed, based on the contraction mapping principle which can be used to prove existence and uniqueness for the quadratic equation x = y + lambdaB(x,x) (1) in a Banach space X; here B: XxX?X is a bounded, symmetric bilinear operator, lambda is a positive parameter and y as a subset of X is fixed. The following is the main result. Theorem. Suppose F: XxX?X is a bounded, symmetric bilinear operator and that the equation z = y + lambdaF(z,z) has a solution z/sup */ of sufficiently small norm. Then equation (1) has a unique solution in a certain closed ball centered at z/sup */. Applications. The theorem is applied to the famous Chandrasekhar equation and to the Anselone-Moore system which are of the form (1) above and yields existence and uniqueness for a solution of (1) for larger values of lambda than previously known, as well as more accurate information on the location of solutions

1984-01-01

349

Microwave imaging of elliptically shaped dielectric cylinders by means of an Lp Banach-space inversion algorithm  

Science.gov (United States)

Microwave imaging apparatuses have become very important tools in the framework of imaging systems. However, particular care must be taken when developing the data-processing algorithm needed to solve the underlying nonlinear and ill-posed inverse problem. Usually, regularization techniques developed in the framework of Hilbert spaces are used. In this paper, a new approach based on a regularization in the framework of Lp Banach spaces is considered, and its performances are evaluated by considering a reference canonical target with elliptical cross section.

Estatico, C.; Fedeli, A.; Pastorino, M.; Randazzo, A.

2013-07-01

350

Bundles of Banach algebras  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We study bundles of Banach algebras π:A→X, where each fiber Ax=π−1({x}) is a Banach algebra and X is a compact Hausdorff space. In the case where all fibers are commutative, we investigate how the Gelfand representation of the section space algebra Γ(π) relates to the Gelfand representation of the fibers. In the general case, we investigate how adjoining an identity to the bundle π:A→X relates to the...

Kitchen, J. W.; Robbins, D. A.

1994-01-01

351

Strong Convergence Theorems of Modified Ishikawa Iterations for Countable Hemi-Relatively Nonexpansive Mappings in a Banach Space  

Directory of Open Access Journals (Sweden)

Full Text Available We prove some strong convergence theorems for fixed points of modified Ishikawa and Halpern iterative processes for a countable family of hemi-relatively nonexpansive mappings in a uniformly convex and uniformly smooth Banach space by using the hybrid projection methods. Moreover, we also apply our results to a class of relatively nonexpansive mappings, and hence, we immediately obtain the results announced by Qin and Su's result (2007, Nilsrakoo and Saejung's result (2008, Su et al.'s result (2008, and some known corresponding results in the literatures.

Narin Petrot

2009-01-01

352

ON THE LOCAL CONVERGENCE OF A MIDPOINT METHOD IN BANACH SPACES UNDER A GAMMA-TYPE CONDITION  

Scientific Electronic Library Online (English)

Full Text Available SciELO Chile | Language: English Abstract in english In this study we are concerned with the problem of approximating a locally unique solution of an operator equation in a Banach space setting using the midpoint method, introduced by us in [5], [6]. Here, we use gamma-type condition to provide a local convergence analysis. Our results compare favorab [...] ly with the relevant ones in [9], [11], [12]-[14]- In particular our radius of convergence is larger. Numerical examples are also provided.

Ioannis K, Argyros.

353

A strong convergence theorem on solving common solutions for generalized equilibrium problems and fixed-point problems in Banach space  

Directory of Open Access Journals (Sweden)

Full Text Available Abstract In this paper, the common solution problem (P1 of generalized equilibrium problems for a system of inverse-strongly monotone mappings and a system of bifunctions satisfying certain conditions, and the common fixed-point problem (P2 for a family of uniformly quasi-?-asymptotically nonexpansive and locally uniformly Lipschitz continuous or uniformly Hlder continuous mappings are proposed. A new iterative sequence is constructed by using the generalized projection and hybrid method, and a strong convergence theorem is proved on approximating a common solution of (P1 and (P2 in Banach space. 2000 MSC: 26B25, 40A05

Qu De-ning

2011-01-01

354

The Generalized Gronwall Inequality and Its Application to Periodic Solutions of Integrodifferential Impulsive Periodic System on Banach Space  

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Full Text Available Abstract This paper deals with a class of integrodifferential impulsive periodic systems on Banach space. Using impulsive periodic evolution operator given by us, the -periodic PC-mild solution is introduced and suitable Poincar operator is constructed. Showing the compactness of Poincar operator and using a new generalized Gronwall's inequality with impulse, mixed type integral operators and -norm given by us, we utilize Leray-Schauder fixed point theorem to prove the existence of -periodic PC-mild solutions. Our method is much different from methods of other papers. At last, an example is given for demonstration.

Wei W

2008-01-01

355

Iterative methods for nonlinear ill-posed problems in Banach spaces: convergence and applications to parameter identification problems  

International Nuclear Information System (INIS)

In this paper, we study convergence of two different iterative regularization methods for nonlinear ill-posed problems in Banach spaces. One of them is a Landweber type iteration, the other one the iteratively regularized GaussNewton method with an a posteriori chosen regularization parameter in each step. We show that a discrepancy principle as a stopping rule renders these iteration schemes regularization methods, i.e., we prove their convergence as the noise level tends to zero. The theoretical findings are illustrated by two parameter identification problems for elliptic PDEs

2009-06-01

356

Morse theory on banach manifolds  

International Nuclear Information System (INIS)

The Morse Theory of critical points was extended by Palais and Smale to a certain class of functions on Hilbert manifolds. However, there are many variational problems in a nonlinear setting which for technical reasons are posed not on Hilbert but on Banach manifolds of mappings. This paper introduces a concept of a multivalued gradient vector field for a function defined on a Banach manifold. Using this concept, the Morse theory is generalized to some kind of Banach manifolds. The first chapter gives a definition of nondegeneracy of critical points for a real valued function defined on a reflexive Banach manifold, and then a handle-body decomposition theorem and Morse inequalities for this manifold are obtained. The second chapter proves the existence of solutions for a differential inclusion for a so-called accretive multi-valued mapping on a Finsler manifold. The third chapter introduces a definition of nondegeneracy of critical points for a real valued function defined on a general Banach manifold and, furthermore, generalizes the Morse handle-body decomposition theorem and the Morse inequalities to the Banach manifold

1986-01-01

357

Convergence of Path and Approximation of Common Element of Null Spaces of Countably Infinite Family of m-Accretive Mappings in Uniformly Convex Banach Spaces  

Directory of Open Access Journals (Sweden)

Full Text Available We prove path convergence theorems and introduce a new iterative sequence for a countably infinite family of m-accretive mappings and prove strong convergence of the sequence to a common zero of these operators in uniformly convex real Banach space. Consequently, we obtain strong convergence theorems for a countably infinite family of pseudocontractive mappings. Our theorems extend and improve some important results which are announced recently by various authors.

Y. Shehu

2009-01-01

358

Weak and strong convergence of an implicit iterative process with errors for a finite family of asymptotically quasi $I-$nonexpansive mappings in Banach space  

CERN Document Server

In this paper we prove the weak and strong convergence of the implicit iterative process with errors to a common fixed point of a finite family $\\{T_j\\}_{i=1}^N$ of asymptotically quasi $I_j-$nonexpansive mappings as well as a family of $\\{I_j\\}_{j=1}^N$ of asymptotically quasi nonexpansive mappings in the framework of Banach spaces.

Mukhamedov, Farrukh

2010-01-01

359

Weak Convergence and Banach Space-Valued Functions: Improving the Stability Theory of Feynman's Operational Calculi  

Energy Technology Data Exchange (ETDEWEB)

In this paper we investigate the relation between weak convergence of a sequence {l_brace}{mu}{sub n}{r_brace} of probability measures on a Polish space S converging weakly to the probability measure {mu} and continuous, norm-bounded functions into a Banach space X. We show that, given a norm-bounded continuous function f:S{yields}X, it follows that lim{sub n{infinity}} {integral}{sub S}f, d{mu}{sub n} = {integral}{sub S}f, d{mu} -the limit one has for bounded and continuous real (or complex)-valued functions on S. This result is then applied to the stability theory of Feynman's operational calculus where it is shown that the theory can be significantly improved over previous results.

Nielsen, Lance, E-mail: lnielsen@creighton.edu [Creighton University, Department of Mathematics (United States)

2011-12-15

360

Some estimates for the Banach space norms in the von Neumann algebras associated with the Berezin's quantization of compact Riemann  

CERN Multimedia

Let \\G be any cocompact, discrete subgroup of \\pslr. In this paper we find estimates for the predual and the uniform Banach space norms in the von Neumann algebras associated with the Berezin' s quantization of a compact Riemann surface \\Bbb D/\\G. As a corollary for large values of the deformation parameter 1/h, these von Neumann algebras are isomorphic. Using the results in [AS], [AC], [GHJ] on the von Neumann dimension of the Hilbert spaces in the discrete series of unitary representations of PSL(2,\\Bbb R), as left modules over \\Gamma we deduce that the fundamental group ([MvN]) of the von Neumann \\Cal L(\\Gamma) contains the positive rational numbers. Equivalently, this proves that the algebras \\Cal L(\\Gamma)\\otimes M_n(\\Bbb C), are isomorphic for all n.

Radulescu, F G

1995-01-01

 
 
 
 
361

On the S-transform over a Banach algebra  

CERN Document Server

The S-transform is shown to satisfy a specific twisted multiplicativity property for free random variables in a B-valued Banach noncommutative probability space, for an arbitrary unital complex Banach algebra B.

Dykema, K J

2005-01-01

362

Approximation of Fixed Points of Asymptotically k strict Pseudocontractive Mapping in the Intermediate Sense in Banach Space  

Directory of Open Access Journals (Sweden)

Full Text Available Let E be a real Banach space and C be a nonempty closed convex subset of E.T:C?C is a uniformly LLipschitz asymptotically k strict pseudocontractive mapping in the intermediate sense and *SymboleB@n=1*be any given point,*is the modified Mann iterative sequence with errors defined by *is nonempty and bounded?under some appropriate restricted conditions?a necessary and sufficient condition for*converges strongly to a fixed point of*.After removing the condition that FDK(T is bounded?under the same restricted conditions on the parameters?the modified Mann iterative sequence* converges strongly to a fixed point of if and only if *.(* Indicates a formula, please see the full text

XIANG Chang-he

2013-01-01

363

Asymptotic behavior of almost-orbits of reversible semigroups of non-Lipschitzian mappings in Banach spaces  

Directory of Open Access Journals (Sweden)

Full Text Available Let C be a nonempty closed convex subset of a uniformly convex Banach space E with a Fréchet differentiable norm, G a right reversible semitopological semigroup, and 𝒮={S(t:t∈G} a continuous representation of G as mappings of asymptotically nonexpansive type of C into itself. The weak convergence of an almost-orbit {u(t:t∈G} of 𝒮={S(t:t∈G} on C is established. Furthermore, it is shown that if P is the metric projection of E onto set F(S of all common fixed points of 𝒮={S(t:t∈G}, then the strong limit of the net {Pu(t:t∈G} exists.

Jong Seo Park

1997-03-01

364

Strong Convergence of Cesàro Mean Iterations for Nonexpansive Nonself-Mappings in Banach Spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Let E be a real uniformly convex Banach space which admits a weakly sequentially continuous duality mapping from E to E*, C a nonempty closed convex subset of E which is also a sunny nonexpansive retract of E, and T:C→E a non-expansive nonself-mapping with F(T)≠∅. In this paper, we study the strong convergence of two sequences generated by xn+1=αnx+(1−αn)(1/n+1)∑j=0n(PT)jxn and yn+1=(1/n+1)∑j=0nP(α...

2007-01-01

365

Weak and strong convergence theorems of a multistep iteration to a common fixed point of a family of nonself asymptotically nonexpansive mappings in banach spaces  

Scientific Electronic Library Online (English)

Full Text Available SciELO Chile | Language: English Abstract in spanish En este artculo definimos un esquema de multi paso iterativo con errores que involucran una familia de aplicaciones no expansivas y no auto asintticamente en espacios deBanach. Una retraccin se ha usado en la construccin de la iteracin. Probamos convergencias dbiles y fuertes de las iteracione [...] s a puntos fijos clsicos de la familia de aplicaciones no expansivas no auto asintticamente. Hemos usado varios conceptos de geometra en espacios de Banach. Nuestro resultado mejora y extiende algunos resultados recientes. Abstract in english In this paper we have defined a multistep iterative scheme with errors involving a family of asymptotically nonexpansive nonself mappings in Banach spaces. A retraction has been used in the construction of theiteration. We prove here weak and strong convergences of the iteration to common fixed poin [...] ts of the family of asymptotically nonexpansive nonself mappings. We have used several concepts of Banach space geometry. Our results improve and extend some recent results.

Shrabani, Banerjee; Binayak S, Choudhury.

366

Ring homomorphisms on real Banach algebras  

Directory of Open Access Journals (Sweden)

Full Text Available Let B be a strictly real commutative real Banach algebra with the carrier space ΦB. If A is a commutative real Banach algebra, then we give a representation of a ring homomorphism ρ:A→B, which needs not be linear nor continuous. If A is a commutative complex Banach algebra, then ρ(A is contained in the radical of B.

Sin-Ei Takahasi

2003-08-01

367

Positive Solutions of Singular Multipoint Boundary Value Problems for Systems of Nonlinear Second-Order Differential Equations on Infinite Intervals in Banach Spaces  

Directory of Open Access Journals (Sweden)

Full Text Available The cone theory together with Mnch fixed point theorem and a monotone iterative technique is used to investigate the positive solutions for some boundary problems for systems of nonlinear second-order differential equations with multipoint boundary value conditions on infinite intervals in Banach spaces. The conditions for the existence of positive solutions are established. In addition, an explicit iterative approximation of the solution for the boundary value problem is also derived.

Xingqiu Zhang

2009-01-01

368

Positive Solutions of Singular Multipoint Boundary Value Problems for Systems of Nonlinear Second-Order Differential Equations on Infinite Intervals in Banach Spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

The cone theory together with Mnch fixed point theorem and a monotone iterative technique is used to investigate the positive solutions for some boundary problems for systems of nonlinear second-order differential equations with multipoint boundary value conditions on infinite intervals in Banach spaces. The conditions for the existence of positive solutions are established. In addition, an explicit iterative approximation of the solution for the boundary value problem is also derived.

2009-01-01

369

Positive Solutions of Singular Multipoint Boundary Value Problems for Systems of Nonlinear Second-Order Differential Equations on Infinite Intervals in Banach Spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

The cone theory together with Mnch fixed point theorem and a monotone iterative technique is used to investigate the positive solutions for some boundary problems for systems of nonlinear second-order differential equations with multipoint boundary value conditions on infinite intervals in Banach spaces. The conditions for the existence of positive solutions are established. In addition, an explicit iterative approximation of the solution for the boundary value problem is also d...

2009-01-01

370

ON OPERATOR IDEALS DEFINED BY A REFLEXIVE ORLICZ SEQUENCE SPACE  

Directory of Open Access Journals (Sweden)

Full Text Available Classical theory of tensornorms and operator ideals studies mainlythose defined by means of sequence spaces ..p. Considering Orlicz sequence spaces as natural generalization of ..p spaces, in a previous paper [12] an Orlicz sequence space was used to define a tensornorm, and characterize minimal and maximal operator ideals associated, by using local techniques. Now, in this paper we give a new characterization of the maximal operator ideal to continue our analysis of some coincidences among such operator ideals. Finally we prove some new metric properties of tensornorm mentioned above

J LPEZ

2006-12-01

371

Some results on the span of families of Banach valued independent, random variables  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Let E be a Banach space, and let (Ω,ℱ,P) be a probability space. If L1(Ω) contains an isomorphic copy of L1[0,1] then in LEP(Ω)(1≤P<∞), the closed linear span of every sequence of independent, E valued mean zero random variables has infinite codimension. If E is reflexive or B-convex and 1

Rohan Hemasinha

1991-01-01

372

(0,2) Target-space duality, CICYs and reflexive sheaves  

International Nuclear Information System (INIS)

It is shown that the recently proposed target-space duality for (0,2) models is not limited to models admitting a Landau-Ginzburg description. By studying some generic examples it is established for the broader class of vector bundles over complete intersections in toric varieties. Instead of sharing a common Landau-Ginzburg locus, a pair of dual models agrees in more general non-geometric phases. The mathematical tools for treating reflexive sheaves are provided as well. (orig.)

1998-03-23

373

Banach Lie algebroids  

CERN Document Server

First, we extend the notion of second order differential equations (SODE) on a smooth manifold to anchored Banach vector bundles. Then we define the Banach Lie algebroids as Lie algebroids structures modeled on anchored Banach vector bundles and prove that they form a category.

Anastasiei, Mihai

2010-01-01

374

On non-midpoint locally uniformly rotund normability in Banach spaces  

Directory of Open Access Journals (Sweden)

Full Text Available We will show that if X is a tree-complete subspace of ℓ∞, which contains c0, then it does not admit any weakly midpoint locally uniformly convex renorming. It follows that such a space has no equivalent Kadec renorming.

A. K. Mirmostafaee

2004-06-01

375

Some results on the span of families of Banach valued independent, random variables  

Directory of Open Access Journals (Sweden)

Full Text Available Let E be a Banach space, and let (Ω,ℱ,P be a probability space. If L1(Ω contains an isomorphic copy of L1[0,1] then in LEP(Ω(1≤P<∞, the closed linear span of every sequence of independent, E valued mean zero random variables has infinite codimension. If E is reflexive or B-convex and 1reflexive.

Rohan Hemasinha

1991-06-01

376

Functional analysis and applied optimization in Banach spaces applications to non-convex variational models  

CERN Document Server

This book introduces the basic concepts of real and functional analysis. It presents the fundamentals of the calculus of variations, convex analysis, duality, and optimization that are necessary to develop applications to physics and engineering problems. The book includes introductory and advanced concepts in measure and integration, as well as an introduction to Sobolev spaces. The problems presented are nonlinear, with non-convex variational formulation. Notably, the primal global minima may not be attained in some situations, in which cases the solution of the dual problem corresponds to an appropriate weak cluster point of minimizing sequences for the primal one. Indeed, the dual approach more readily facilitates numerical computations for some of the selected models. While intended primarily for applied mathematicians, the text will also be of interest to engineers, physicists, and other researchers in related fields.

Botelho, Fabio

2014-01-01

377

Iterative approximation of the solution of a monotone operator equation in certain Banach spaces  

International Nuclear Information System (INIS)

Let X=Lp (or lp), p ? 2. The solution of the equation Ax=f, f is an element of X is approximated in X by an iteration process in each of the following two cases: (i) A is a bounded linear mapping of X into itself which is also bounded below; and, (ii) A is a nonlinear Lipschitz mapping of X into itself and satisfies ? m |x-y|2, for some constant m > 0 and for all x, y in X, where j is the single-valued normalized duality mapping of X into X* (the dual space of X). A related result deals with the iterative approximation of the fixed point of a Lipschitz strictly pseudocontractive mapping in X. (author). 12 refs

1988-01-01

378

On the perturbation of the group generalized inverse for a class of bounded operators in Banach spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

En este trabajo se estudia la perturbacin de la inversa generalizada grupo en el \tmbito de los operadores lineales y acotados sobre un espacio de Banach \tcomplejo. \tSe establecen, en primer lugar, caracterizaciones de los {1,2}-inversos generalizados de operadores perturbados que verifican una condicin de no singularidad. Posteriormente se caracteriza la clase de operadores perturbados para los cuales existe el operador inverso \tgrupo y verifican ciertas condiciones ...

Castro Gonza?lez, Nieves; Ve?lez Cerrada, Jose? Ygnacio

2008-01-01

379

Banach C*-algebras not containing a subspace isomorphic to C0  

International Nuclear Information System (INIS)

If X is a locally Hausdorff space and C0(X) the Banach algebra of continuous functions defined on X vanishing at infinity, we showed that a subalgebra A of C0(X) is finite dimensional if it does not contain a subspace isomorphic to the Banach space C0 of convergent to zero complex sequences. In this paper we extend this result to noncommutative Banach C*-algebras and Banach* algebras. 10 refs

1989-01-01

380

Remark on application of the Banach metric method to cosmology  

International Nuclear Information System (INIS)

If the cosmological equations can be reduced to the form of a dynamic system, the space of all their solutions is a Banach space. The influence of different parameters on the dynamics of the world models can be easily studied by means of the Banach metric. The method is tested for the Friedman cosmological models perturbed by the bulk viscosity. (author)

1982-01-01

 
 
 
 
381

ANALYSIS OF AN OPERATOR EQUATION WITH THE DIFFERENTIABLE IN BANACH SPACE OPERATOR AND ITS APPLICATION TO THE INVESTIGATION OF REACTOR MODEL DYNAMICS  

Directory of Open Access Journals (Sweden)

Full Text Available An operator equation of the following form?x = z + F(x,where z - an element of Banach space X and F(x?X for x?D?X, is investigated. In the cas of m-order differentiable operator F (m>3, conditions of existence and uniqueness of a solution of considered equation are formulated and an estimation of the norm of this solution as a function of the norm z is obtained.The results of theoretical analysis are applied to the point reactor model with nonlinear, temperature-type reactivity feedback. The conditions of the asymptotic stability for the autonomous system as well as for the system including the external reactivity oscilations, are formulated.

Micha? Podowski

1977-01-01

382

Moro reflex  

Science.gov (United States)

Startle response; Startle reflex; Embrace reflex ... Your baby's doctor will check for this reflex right after birth and during well-child visits. To see the Moro reflex, the child will be placed face up on a soft, ...

383

Sectional representation of Banach modules and their multipliers  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Let X be a Banach module over the commutative Banach algebra A with maximal ideal space Δ. We show that there is a norm-decreasing representation of X as a space of bounded sections in a Banach bundle π:ℰ→Δ, whose fibers are quotient modules of X. There is also a representation of M(X), the space of multipliers T:A→X, as a space of sections in the same bundle, but this representation may not be continuous. These sectional repre...

Im, Terje H.; Robbins, D. A.

2003-01-01

384

Space and time dependent properties of the virtual cathode in a reflex-type pulsed ion diode (virtual cathode in a reflex-type pulsed ion diode)  

International Nuclear Information System (INIS)

Properties of a virtual cathode in a pulsed ion diode composed of an insulator-mesh anode and a metal-mesh cathode were studied experimentally at anode voltages below 360kV. Potential distribution in the virtual cathode side was measured with an insulated electrostatic potential probe, and ion beam currents in virtual and real cathode sides were measured with biased ion collectors. A loss parameter for the electron current at the virtual cathode was evaluated from the measured electron current values by using relations derived from the one-dimensional Child-Langmuir theory applied to the reflex triode. The ion beam accompanies a considerable amount of electron current, and this influences the stability of the virtual cathode; this perturbation results in variations of ion current with time. Space potentials in the emitted ion beam are given, suggesting an existence of high energy electrons of several keV accelerated by positive space potential of the ion beam. (author)

1982-01-01

385

A Banach Principle for Semifinite von Neumann Algebras  

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Full Text Available Utilizing the notion of uniform equicontinuity for sequences of functions with the values in the space of measurable operators, we present a non-commutative version of the Banach Principle for $L^infty$.

Vladimir Chilin

2006-02-01

386

A noncommutative version of the Banach-Stone Theorem  

CERN Document Server

In this paper, we extend the Banach-Stone theorem to the non commutative case, i.e, we prove that the structure of the liminal $C^{*}$-algebras $\\cal A$ determines the topology of its primitive ideal space.

Bouali, B

2001-01-01

387

Characterization of compact and self-adjoint operators on free Banach spaces of countable type over the complex Levi-Civita field  

Science.gov (United States)

Let be the complex Levi-Civita field and let E be a free Banach space over of countable type. Then E is isometrically isomorphic to c0N,,s:=(xn)n?N:xn?limn-->?|xn|s(n)=0, where s:N-->0,?. If the range of s is contained in \\0, it is enough to study c0N,, which will be denoted by c0() or, simply, c0. In this paper, we define a natural inner product on c0, which induces the sup-norm of c0. Of course, c0 is not orthomodular, so we characterize those closed subspaces of c0 with an orthonormal complement with respect to this inner product; that is, those closed subspaces M of c0 such that c0 = M ? M?. Such a subspace, together with its orthonormal complement, defines a special kind of projection, the so-called normal projection. We present a characterization of such normal projections as well as a characterization of another kind of operators, the compact operators on c0.

Aguayo, Jos; Nova, Miguel; Shamseddine, Khodr

2013-02-01

388

On the structure of Banach algebras associated with automorphisms  

Digital Repository Infrastructure Vision for European Research (DRIVER)

In the present paper we study the structure of a Banach algebra B(A, T_g) generated by a certain Banach algebra $A$ of operators acting in a Banach space D and a group {T_g}_{g \\in G} of isometries of D such that T_g A T^{-1}_g = A. We investigate the interrelations between the existence of the expectation of B(A, T_g) onto A, topological freedom of the automorphisms of A induced by T_g and the dual action of the group G on B(A, T_g). The results obtained are applied to the ...

Lebedev, A.

2002-01-01

389

n-Approximately Weak Amenability of Banach Algebras  

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We introduce new notions of approximate amenability for a Banach algebra A. A Banach algebra A is n-approximately weakly amenable, for n ? N, if every continuous derivation from A into the n-th dual space A(n) is approximately inner. First we examine the relation between m-approximately weak amenability and n-approximately weak amenability for distinct m,n ? N. Then we investigate (2n+1)-approximately weak amenability of module extension Banach algebras. Finally, we give ...

Najafi, H.; Yazdanpanah, T.

2009-01-01

390

Ultrametric Banach algebras  

CERN Multimedia

In this book, ultrametric Banach algebras are studied with the help of topological considerations, properties from affinoid algebras, and circular filters which characterize absolute values on polynomials and make a nice tree structure. The Shilov boundary does exist for normed ultrametric algebras. In uniform Banach algebras, the spectral norm is equal to the supremum of all continuous multiplicative seminorms whose kernel is a maximal ideal. Two different such seminorms can have the same kernel. Krasner-Tate algebras are characterized among Krasner algebras, affinoid algebras, and ultrametri

Escassut, Alain

2003-01-01

391

Isometries between groups of invertible elements in Banach algebras  

CERN Document Server

We show that if $T$ is an isometry (as metric spaces) from an open subgroup of the group of the invertible elements in a unital semisimple commutative Banach algebra onto an open subgroup of the group of the invertible elements in a unital Banach algebra, then $T(1)^{-1}T$ is an isometrical group isomorphism. In particular, $T(1)^{-1}T$ is extended to an isometrical real algebra isomorphism from $A$ onto $B$.

Hatori, Osamu

2009-01-01

392

The higher duals of certain class of Banach algebras  

CERN Document Server

Given a Banach space $A$ and fix a non-zero $\\varphi\\in A^*$ with $\\|\\varphi\\|\\leq 1$. Then the product $a\\cdot b=\\langle\\varphi, a\\rangle\\ b$ turning $A$ into a Banach algebra which will be denoted by $_\\varphi A.$ Some of the main properties of $_\\varphi A$ such as Arens regularity, $n$-weak amenability and semi-simplicity are investigated.

Khoddami, A R

2010-01-01

393

An inner product for a Banach-algebra  

International Nuclear Information System (INIS)

An inner product is defined on a commutative Banach algebra with an essential involution and the resultant inner product space is shown to be a topological algebra. Several conditions for its completeness are established and moreover, a decomposition theorem is proved. It is shown that every commutative Banach algebra with an essential involution has an auxiliary norm which turns it into an A*-algebra. (author). 6 refs

1988-01-01

394

Intuitionistic Fuzzy Banach Algebra  

CERN Document Server

Intuitionistic fuzzy Banach algebra is introduced and a few properties of it is studied. The properties of invertible elements and relation among invertible elements, open set, closed set are emphasized. Topological divisors of zero is defined and its relation with closed set are studied.

Dinda, Bivas; Bera, U K

2010-01-01

395

Impulsive moving mirror model and the stability of linear homogeneous differential equations with impulse effect in a Banach space.  

Science.gov (United States)

From a special class of systems has been used the linear homogeneous differential equations with impulse effect in Minkowski space field theory with time dependent boundary conditions, i.e. those of moving mirrors. The field theoretical approach for studi...

S. I. Kostadinov G. Petrov

1992-01-01

396

Module amenability for Banach modules  

Scientific Electronic Library Online (English)

Full Text Available SciELO Chile | Language: English Abstract in spanish Se estudia el mdulo de receptividad de los mdulos de Banach. Esta es una generalizacin natural de la receptividad de Johnson de las lgebras de Banach. Como ejemplo se muestra que para un grupo abeliano discreto G l p(G) es receptivo como un G l p(G)- mdulo, si y slo si G es receptivo, donde l [...] (G) es un lgebra de Banach con producto punto. Abstract in english We study the module amenability of Banach modules. This is a natural generalization of Johnson?s amenability of Banach algebras. As an example we show that for a discrete abelian group G, l p(G) is amenable as an l(G)-module if and only if G is amenable, where l(G) is a Banach algebra with pointwi [...] se multiplication.

Ebrahimi Bagha, D; Amini, M.

397

Module amenability for Banach modules  

Directory of Open Access Journals (Sweden)

Full Text Available We study the module amenability of Banach modules. This is a natural generalization of Johnsons amenability of Banach algebras. As an example we show that for a discrete abelian group G, l p(G is amenable as an l(G-module if and only if G is amenable, where l(G is a Banach algebra with pointwise multiplication.Se estudia el mdulo de receptividad de los mdulos de Banach. Esta es una generalizacin natural de la receptividad de Johnson de las lgebras de Banach. Como ejemplo se muestra que para un grupo abeliano discreto G l p(G es receptivo como un G l p(G- mdulo, si y slo si G es receptivo, donde l(G es un lgebra de Banach con producto punto.

D Ebrahimi Bagha

2011-06-01

398

Modification of Otolith-Ocular Reflexes, Motion Perception and Manual Control During Variable Radius Centrifugation Following Space Flight  

Science.gov (United States)

Two joint ESA-NASA studies are examining changes in otolith-ocular reflexes and motion perception following short duration space flights, and the operational implications of post-flight tilt-translation ambiguity for manual control performance. Vibrotactile feedback of tilt orientation is also being evaluated as a countermeasure to improve performance during a closed-loop nulling task. Data is currently being collected on astronaut subjects during 3 preflight sessions and during the first 8 days after Shuttle landings. Variable radius centrifugation is utilized to elicit otolith reflexes in the lateral plane without concordant roll canal cues. Unilateral centrifugation (400 deg/s, 3.5 cm radius) stimulates one otolith positioned off-axis while the opposite side is centered over the axis of rotation. During this paradigm, roll-tilt perception is measured using a subjective visual vertical task and ocular counter-rolling is obtained using binocular video-oculography. During a second paradigm (216 deg/s, less than 20 cm radius), the effects of stimulus frequency (0.15 - 0.6 Hz) are examined on eye movements and motion perception. A closed-loop nulling task is also performed with and without vibrotactile display feedback of chair radial position. Data collection is currently ongoing. Results to date suggest there is a trend for perceived tilt and translation amplitudes to be increased at the low and medium frequencies on landing day compared to pre-flight. Manual control performance is improved with vibrotactile feedback. One result of this study will be to characterize the variability (gain, asymmetry) in both otolith-ocular responses and motion perception during variable radius centrifugation, and measure the time course of post-flight recovery. This study will also address how adaptive changes in otolith-mediated reflexes correspond to one's ability to perform closed-loop nulling tasks following G-transitions, and whether manual control performance can be improved with vibrotactile feedback of orientation.

Wood, Scott J.; Clarke, A. H.; Rupert, A. H.; Harm, D. L.; Clement, G. R.

2009-01-01

399

Strong convergence theorems for a common fixed point of a finite family of Bregman weak relativity nonexpansive mappings in reflexive Banach spaces.  

Science.gov (United States)

We introduce an iterative process for finding an element of a common fixed point of a finite family of Bregman weak relatively nonexpansive mappings. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators. PMID:24757423

Zegeye, Habtu; Shahzad, Naseer

2014-01-01

400

Strong Convergence Theorems for a Common Fixed Point of a Finite Family of Bregman Weak Relativity Nonexpansive Mappings in Reflexive Banach Spaces  

Science.gov (United States)

We introduce an iterative process for finding an element of a common fixed point of a finite family of Bregman weak relatively nonexpansive mappings. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators.

2014-01-01

 
 
 
 
401

C-orbit reflexive operators  

CERN Multimedia

We introduce the notion of C-orbit reflexivity and study its properties. An operator on a finite-dimensional space is C-orbit reflexive if and only if the two largest blocks in its Jordan form corresponding to nonzero eigenvalues with the largest modulus differ in size by at most one. Most of the proofs of our results in infinite dimensions are obtained from purely algebraic results we obtain from linear-algebraic analogs of C-orbit reflexivity.

Hadwin, Don; McHugh, Michael; Yousefi, Hassan

2010-01-01

402

Almost normal operators mod Hilbert-Schmidt and the K-theory of the Banach algebras $E\\Lambda(\\Omega)$  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Is there a mod Hilbert-Schmidt analogue of the BDF-theorem, with the Pincus g-function playing the role of the index ? We show that part of the question is about the K-theory of certain Banach algebras. These Banach algebras, related to Lipschitz functions and dirichlet algebras have nice Banach space duality properties. Moreover their corona algebras are C*-algebras.

Voiculescu, Dan-virgil

2011-01-01

403

Constructive Theory of Banach algebras  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We present a way to organize a constructive development of the theory of Banach algebras, inspired by works of Cohen, de Bruijn and Bishop. We illustrate this by giving elementary proofs of Wiener's result on the inverse of Fourier series and Wiener's Tauberian Theorem, in a sequel to this paper we show how this can be used in a localic, or point-free, description of the spectrum of a Banach algebra.

Coquand, Thierry; Spitters, Bas

2010-01-01

404

Multiplicative spectrum of ultrametric Banach algebras of continuous functions  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Let $K$ be an ultrametric complete field and let $E$ be an ultrametric space. Let $A$ be the Banach $K$-algebra of bounded continuous functions from $E$ to $K$ and let $B$ be the Banach $K$-algebra of bounded uniformly continuous functions from $E$ to $K$. Maximal ideals and continuous multiplicative semi-norms on $A$ (resp. on $B$) are studied by defining relations of stickness and contiguousness on ultrafilters that are equivalence relations. So, the maximal spectrum of $A$ (resp. of $B$) i...

Escassut, Alain; Mainetti, Nicolas

2010-01-01

405

Spherical isometries are reflexive  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Let H be a complex Hilbert space. A commuting system T=(T_{1},...,T_{n}) of bounded linear operators on H is called a spherical isometry if T_{1}^{\\star}T_{1}+T_{2}^{\\star}T_{2}+\\cdots+T_{n}^{\\star}T_{n}=1_{H}. In this note we prove that each spherical isometry is reflexive.

2004-01-01

406

The Banach-Tarski paradox  

CERN Document Server

The Banach-Tarski paradox is a most striking mathematical construction: it asserts that a solid ball may be taken apart into finitely many pieces that can be rearranged using rigid motions to form a ball twice as large as the original. This volume explore

Wagon, Stan

1985-01-01

407

ZAG-Otolith: Modification of Otolith-Ocular Reflexes, Motion Perception and Manual Control during Variable Radius Centrifugation Following Space Flight  

Science.gov (United States)

Two joint ESA-NASA studies are examining changes in otolith-ocular reflexes and motion perception following short duration space flights, and the operational implications of post-flight tilt-translation ambiguity for manual control performance. Vibrotactile feedback of tilt orientation is also being evaluated as a countermeasure to improve performance during a closed-loop nulling task. METHODS. Data is currently being collected on astronaut subjects during 3 preflight sessions and during the first 8 days after Shuttle landings. Variable radius centrifugation is utilized to elicit otolith reflexes in the lateral plane without concordant roll canal cues. Unilateral centrifugation (400 deg/s, 3.5 cm radius) stimulates one otolith positioned off-axis while the opposite side is centered over the axis of rotation. During this paradigm, roll-tilt perception is measured using a subjective visual vertical task and ocular counter-rolling is obtained using binocular video-oculography. During a second paradigm (216 deg/s, reflexes correspond to one's ability to perform closed-loop nulling tasks following G-transitions, and whether manual control performance can be improved with vibrotactile feedback of orientation.

Wood, S. J.; Clarke, A. H.; Rupert, A. H.; Harm, D. L.; Clement, G. R.

2009-01-01

408

Asymptotically Pseudocontractions, Banach Operator Pairs and Best Simultaneous Approximations  

Directory of Open Access Journals (Sweden)

Full Text Available The existence of common fixed points is established for the mappings where is asymptotically -pseudo-contraction on a nonempty subset of a Banach space. As applications, the invariant best simultaneous approximation and strong convergence results are proved. Presented results are generalizations of very recent fixed point and approximation theorems of Khan and Akbar (2009, Chen and Li (2007, Pathak and Hussain (2008, and several others.

Hussain N

2011-01-01

409

Chinese Reflexive Ziji: Syntactic Reflexes vs. Nonsyntactic Reflexes.  

Science.gov (United States)

Proposes that the distinction between syntactic and nonsyntactic use of reflexives is not necessarily one of lexical ambiguity, positing one type of referentially dependent element (reflexives) which have two options for being related to their antecedents (syntactic binding and discourse conference). The paper focuses on Chinese reflexive ziji and

Pollard, Carl; Xue, Ping

1998-01-01

410

Peripheral or Local Reflexes.  

Science.gov (United States)

Contents: Basic histological data on sensory-nerve endings in the internal organs and the possibility of reflex-arc completion in the peripheral ganglia; Peripheral, or local reflexes and axon reflexes; Observations on isolated pelvic and digestive organs...

M. V. Sergievskii

1967-01-01

411

[Oculorespiratory reflex].  

Science.gov (United States)

The lack of interest about oculorespiratory reflex (ORR) in surgery and experimental studies is obvious. However the authors insist on the importance of its clinical traduction. The purpose of this study is to determinate an experimental model with titration of stimulus (pressure or traction) and therapeutic test. Our first Results prove the clinic entity of O.R.R. In first conclusion, we can insist on the importance of ventilatory assistance during squint surgery and on the monitoring of PE CO2 and Sa O2. PMID:2225259

Thirion, B; Marchal, F; Ptry, L; George, J L; Crance, J P; Haberer, J P

1990-01-01

412

A note on Banach algebras that are not isomorphic to a group algebra Una nota sobre lgebras de Banach no isomorfas a una lgebra de grupos  

Directory of Open Access Journals (Sweden)

Full Text Available It is proved in this paper that several classical Banach algebras are not isomorphic to a group algebra. These algebras includes C(K algebras where K is a compact Hausdorff space. In the case of amalgams, we give conditions for an amalgam to be a group algebra.En este artculo se prueba que algunas lgebras de Banach clsicas no son isomorfas a un lgebra de grupo. Estas lgebras incluyen a las lgebras C(K donde K es un espacio de Hausdorff Compacto. En el caso de las amalgamas, damos condiciones para que una amalgama sea un lgebra de grupo.

DIOMEDES BARCENAS

413

Reflexives in Veracruz Huastec.  

Science.gov (United States)

A study examines various Huastec clause types that are reflexive in some sense, including ordinary reflexives, which involve co-reference. Two mutually exclusive morphosyntactic devices are used in Huastec: reflexive pronouns and verbal morphology. In this way, Huastec is like various European languages. Clauses involving reflexive pronouns and

Constable, Peter G.

414

Bounded Hochschild cohomology of Banach algebras with a matrix-like structure  

CERN Document Server

Let B be a unital Banach algebra. A projection in B which is equivalent to the identitity may give rise to a matrix-like structure on any two-sided ideal A in B. In this set-up we prove a theorem to the effect that the bounded Hochschild cohomology H^n(A,A^*) vanishes for all n>=1. The hypothesis of this theorem involve (i) strong H-unitality of A, (ii) a growth condition on diagonal matrices in A, (iii) an extension of A in B with trivial bounded simplicial homology. As a corollary we show that if X is an infinite dimensional Banach space with the bounded approximation property, L_1(\\mu,\\Omega) is an infinite dimensional L_1-space, and A is the Banach algebra of approximable operators on L_p(X,\\mu,\\Omega), (1==0.

Gronbaek, N

2003-01-01

415

A note on the L-fuzzy Banach's contraction principle  

International Nuclear Information System (INIS)

Recently, Alaca et al. [Alaca C, Turkoglu D, Yildiz C. Fixed points in intuitionistic fuzzy metric spaces. Chaos, Solitons and Fractals 2006;29:10738] proved fuzzy Banach fixed point theorem in intuitionistic fuzzy metric spaces and Saadati [Saadati R. Notes to the paper 'fixed points in intuitionistic fuzzy metric spaces' and its generalization to L-fuzzy metric spaces. Chaos, Solitions and Fractals 2008;35:80-176] extended it in generalized fuzzy metric spaces. The purpose of this paper is to give a correct proof of the main result in Saadati [Saadati R. Notes to the paper 'fixed points in intuitionistic fuzzy metric spaces' and its generalization to L-fuzzy metric spaces. Chaos, Solitions and Fractals 2008;35:80-176].

2009-09-15

416

Tensor products of commutative Banach algebras  

Directory of Open Access Journals (Sweden)

Full Text Available Let A1, A2 be commutative semisimple Banach algebras and A1⊗∂A2 be their projective tensor product. We prove that, if A1⊗∂A2 is a group algebra (measure algebra of a locally compact abelian group, then so are A1 and A2. As a consequence, we prove that, if G is a locally compact abelian group and A is a comutative semi-simple Banach algebra, then the Banach algebra L1(G,A of A-valued Bochner integrable functions on G is a group algebra if and only if A is a group algebra. Furthermore, if A has the Radon-Nikodym property, then the Banach algebra M(G,A of A-valued regular Borel measures of bounded variation on G is a measure algebra only if A is a measure algebra.

Shobha Madan

1982-09-01

417

Dunford-Pettis sets in Banach lattices  

Directory of Open Access Journals (Sweden)

Full Text Available We study the class of Dunford-Pettis sets in Banach lattices. In particular, we establish some sufficient conditions for which a Dunford-Pettis set is relatively weakly compact (resp. relatively compact

B. Aqzzouz

2012-09-01

418

The structure of homomorphisms from Banach algebras of differentiable functions into finite dimensional Banach algebras  

Directory of Open Access Journals (Sweden)

Full Text Available We show that the structure of continuous and discontinuous homomorphisms from the Banach algebra Cn[0,1] of n times continuously differentiable functions on the unit interval [0,1] into finite dimensional Banach algebras is completely determined by higher point derivations.

Viet Ngo

1990-06-01

419

Spectrum of Weighted Composition Operators. Part II. Weighted composition operators on subspaces of Banach lattices  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We describe the spectrum of weighted $d$-isomorphisms of Banach lattices restricted on closed subspaces that are "rich" enough to preserve some "memory" of the order structure of the original lattice. The examples include (but are not limited to) weighted isometries of Hardy spaces on the polydisk and unit ball in $\\mathds{C}^n$.

Kitover, Arkady

2012-01-01

420

Embodied Self-Reflexivity  

Science.gov (United States)

Drawing on G. H. Mead and Merleau-Ponty, this paper aims to extend our understanding of self-reflexivity beyond the notion of a discursive, abstract, and symbolic process. It offers a framework for embodied self-reflexivity, which anchors the self in the reflexive capacity of bodily sensations. The data consist of two years of ethnographic

Pagis, Michal

2009-01-01

 
 
 
 
421

ON UNICYCLIC REFLEXIVE GRAPHS  

Directory of Open Access Journals (Sweden)

Full Text Available A simple graph is said to be reflexive if the second largest eigenvalue of its (0, 1-adjacency matrix does not exceed 2. Based on some recent results on reflexive graphs with more cycles and some new observations, we construct in this paper several classes of maximal unicyclic reflexive graphs.

Zoran Radosavljevi?

2007-04-01

422

On Peano's theorem in Banach spaces.  

Czech Academy of Sciences Publication Activity Database

. Ro?. 249, ?. 12 (2010), s. 3342-3351. ISSN 0022-0396Grant CEP: GA AV ?R IAA100190801Vzkumn zm?r: CEZ:AV0Z10190503Kl?ov slova: diferential equationsKd oboru RIV: BA - Obecn matematikaImpakt faktor: 1.261, rok: 2010

Hjek, Petr Pavel; Johanis, M.

423

Regularity of difference equations on Banach spaces  

CERN Document Server

This work introduces readers to the topic of maximal regularity for difference equations. The authors systematically present the method of maximal regularity, outlining basic linear difference equations along with relevant results. They address recent advances in the field, as well as basic semigroup and cosine operator theories in the discrete setting. The authors also identify some open problems that readers may wish to take up for further research. This book is intended for graduate students and researchers in the area of difference equations, particularly those with advance knowledge of and interest in functional analysis.

Agarwal, Ravi P; Lizama, Carlos

2014-01-01

424

Generalized Monotone Operators in Banach Spaces.  

Science.gov (United States)

The concept of F-monotonicity was first introduced by Kato and this generalizes the notion of monotonicity introduced by Minty. The purpose of this paper is to define various types of F-monotonicities and discuss the relationships among them. (author). 6 ...

S. Nanda

1988-01-01

425

On dominated polynomials between Banach spaces  

CERN Document Server

In this paper, among other results, we prove a conjecture concerning coincidence theorems for dominated polynomials. We also obtain an abstract version of Pietsch Domination Theorem (PDT) which unifies and generalizes several different nonlinear approaches; our result recovers, as a particular case, the well-known PDT for dominated multilinear mappings.

Botelho, Geraldo; Rueda, Pilar

2008-01-01

426

Complemented subspaces of spaces obtained by interpolation  

Digital Repository Infrastructure Vision for European Research (DRIVER)

If Z is a quotient of a subspace of a separable Banach space X, and V is any separable Banach space, then there is a Banach couple (A_0,A_1) such that A_0 and A_1 are isometric to $X\\oplus V$, and any intermediate space obtained using the real or complex interpolation method contains a complemented subspace isomorphic to Z. Thus many properties of Banach spaces, including having non-trivial cotype, having the Radon-Nikodym property, and having the analytic unconditional mart...

Garling, D. J. H.; Montgomery-smith, Stephen J.

1990-01-01

427

Banach representations and affine compactifications of dynamical systems  

CERN Document Server

To every Banach space V we associate a compact right topological affine semigroup E(V). We show that a separable Banach space V is Asplund if and only if E(V) is metrizable, and it is Rosenthal (i.e. it does not contain an isomorphic copy of $l_1$) if and only if E(V) is a Rosenthal compactum. We study representations of compact right topological semigroups in E(V). In particular, representations of tame and HNS-semigroups arise naturally as enveloping semigroups of tame and HNS (hereditarily non-sensitive) dynamical systems, respectively. As an application we obtain a generalization of a theorem of R. Ellis. A main theme of our investigation is the relationship between the enveloping semigroup of a dynamical system X and the enveloping semigroup of its various affine compactifications Q(X). When the two coincide we say that the affine compactification Q(X) is E-compatible. This is a refinement of the notion of injectivity. We show that distal non-equicontinuous systems do not admit any E-compatible compactif...

Glasner, Eli

2012-01-01

428

Emotionally Colorful Reflexive Games  

CERN Document Server

This study addresses the matter of reflexive control of the emotional states by means of Reflexive Game Theory (RGT). It is shown how to build a bridge between RGT and emotions. For this purpose the Pleasure-Arousal-Dominance (PAD) model is adopted. The major advantages of RGT are its ability to predict human behavior and unfold the entire spectra of reflexion in the human mind. On the other hand, PAD provides ultimate approach to model emotions. It is illustrated that emotions are reflexive processes and, consequently, RGT fused with PAD model is natural solution to model emotional interactions between people. The fusion of RGT and PAD, called Emotional Reflexive Games (ERG), inherits the key features of both components. Using ERG, we show how reflexive control can be successfully applied to model human emotional states. Up to date, EGR is a unique methodology capable of modeling human reflexive processes and emotional aspects simultaneously.

Tarasenko, Sergey

2011-01-01

429

Reflecting on Human Reflexes  

Science.gov (United States)

Students learn about human reflexes, how our bodies react to stimuli and how some body reactions and movements are controlled automatically, without thinking consciously about the movement or responses. In the associated activity, students explore how reflexes work in the human body by observing an involuntary human reflex and testing their own reaction times using dominant and non-dominant hands. Once students understand the stimulus-to-response framework components as a way to describe human reflexes and reactions in certain situations, they connect this knowledge to how robots can be programmed to conduct similar reactions.

GK-12 Program, Computational Neurobiology Center,

430

Nearly Partial Derivations on Banach Ternary Algebras  

Directory of Open Access Journals (Sweden)

Full Text Available Problem statement: In this study, we introduce the concept of a partial ternary derivation from A1 ... An into B, where A1, A2..., An and B are ternary algebras. Conclusion/Recommendations: We prove the generalized Hyers-Ulam stability of partial ternary derivations in Banach ternary algebras.

M. Eshaghi

2010-01-01

431

Nearly Partial Derivations on Banach Ternary Algebras  

Directory of Open Access Journals (Sweden)

Full Text Available Problem statement: In this study, we introduce the concept of a partial ternary derivation from A1 ????? An into B, where A1, A2???, An and B are ternary algebras. Conclusion/Recommendations: We prove the generalized Hyers-Ulam stability of partial ternary derivations in Banach ternary algebras.

M. Eshaghi

2010-01-01

432

Nearly Partial Derivations on Banach Ternary Algebras  

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Problem statement: In this study, we introduce the concept of a partial ternary derivation from A1 ????? An into B, where A1, A2???, An and B are ternary algebras. Conclusion/Recommendations: We prove the generalized Hyers-Ulam stability of partial ternary derivations in Banach ternary algebras.

2010-01-01

433

Nearly Partial Derivations on Banach Ternary Algebras  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Problem statement: In this study, we introduce the concept of a partial ternary derivation from A1 ... An into B, where A1, A2..., An and B are ternary algebras. Conclusion/Recommendations: We prove the generalized Hyers-Ulam stability of partial ternary derivations in Banach ternary algebras.

2010-01-01

434

Character Inner Amenability of Certain Banach Algebras  

CERN Document Server

Character inner amenability for certain class of Banach algebras consist of projective tensor product $A\\hat{\\otimes}B$, Lau product $A\\times_\\theta B$ and module extension $A\\oplus X$ are investigated. Some illuminating examples are also included.

Vishki, H R Ebrahimi

2010-01-01

435

A note on Banach algebras that are not isomorphic to a group algebra / Una nota sobre lgebras de Banach no isomorfas a una lgebra de grupos  

Scientific Electronic Library Online (English)

Full Text Available SciELO Colombia | Language: English Abstract in spanish En este artculo se prueba que algunas lgebras de Banach clsicas no son isomorfas a un lgebra de grupo. Estas lgebras incluyen a las lgebras C(K) donde K es un espacio de Hausdorff Compacto. En el caso de las amalgamas, damos condiciones para que una amalgama sea un lgebra de grupo. [...] Abstract in english It is proved in this paper that several classical Banach algebras are not isomorphic to a group algebra. These algebras includes C(K) algebras where K is a compact Hausdorff space. In the case of amalgams, we give conditions for an amalgam to be a group algebra. [...

DIOMEDES, BARCENAS; WALTER, ESPINOZA; EDIXON, ROJAS.

2008-06-15

436

A G.N.S.-type theorem for a non-involutive Banach algebra  

International Nuclear Information System (INIS)

Given an involutive Banach algebra A with a bounded approximate identity, the elegant construction by Gelfand, Naimark and Segal, associates to each positive linear functional f on A, a triple (H_f, ?_f, ?_f), where H_f is a Hilbert space with scalar product denoted by: , ?_f is a representation of A into L(H_f), the space of bounded linear operators on H_f, ?_f is a cyclic vector in H_f, such that: f(x)=, for all x is an element of A. In this result, the existence of a (multiplicative) involution on A, is central. The aim of this paper is to show that such a construction may be performed for a non-involutive Banach algebra, to obtain a similar triple (H, ?, ?) as above. Moreover, this procedure indeed enables us to associate to the topological dual of any Banach space, a liminary C*-subalgebra of L(H). A notion of compact Hilbert algebras will be introduced, together with a method of construction of a large collection of such spaces. (author). 14 refs

1991-01-01

437

Uniqueness of the maximal ideal of the Banach algebra of bounded operators on C([0,?1])  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Let ?1 be the smallest uncountable ordinal. By a result of Rudin, bounded operators on the Banach space C([0,?1) have a natural representation as [0,?1][0,?1]-matrices. Loy and Willis observed that the set of operators whose final column is continuous when viewed as a scalar-valued function on [0,?1] defines a maximal ideal of codimension one in the Banach algebra B(C([0,?1])) of bounded operators on C([0,?1]). We give a coordinate-free characterization of this ideal and deduce from ...

2012-01-01

438

Stable reflexive sheaves and localization  

CERN Document Server

We study moduli spaces $\\N$ of rank 2 stable reflexive sheaves on $\\PP^3$. Fixing Chern classes $c_1$, $c_2$, and summing over $c_3$, we consider the generating function $G^{refl}(q)$ of Euler characteristics of such moduli spaces. The action of the dense open torus $T$ on $\\PP^3$ lifts to $\\N$ and we classify all sheaves in $\\N^T$. This leads to an explicit expression for $G^{refl}(q)$. Since $c_3$ is bounded below and above, $G^{refl}(q)$ is a polynomial. For $c_1=-1$, we show its leading term is $12c_2 q^{c_{2}^{2}}$. Next, we study moduli spaces of rank 2 stable torsion free sheaves on $\\PP^3$ and consider the generating function $G(q)$ of Euler characteristics of such moduli spaces. We give an expression for this generating function in terms of $G^{refl}(q)$ and Euler characteristics of Quot schemes of certain $T$-equivariant reflexive sheaves. These Quot schemes and their fixed point loci are studied in a sequel with B. Young. The components of these fixed point loci are products of $\\PP^1$'s and give r...

Gholampour, Amin

2013-01-01

439

Factorization and domination properties of operators on Banach lattices = Factorizacin, mayoracin y potencias de operadores positivos en retculos de Banach  

Digital Repository Infrastructure Vision for European Research (DRIVER)

El tema de la Tesis doctoral se encuadra en el campo del Anlisis Funcional, Concretamente dentro de la Teora de Operadores en retculos de Banach. En concreto, se presentan resultados de mayoracin (en el sentido de Dodds-Fremlin) para los ideales de operadores estrictamente singulares y operadores Banach-Saks entre retculos de Banach, mediante la adaptacin de varias tcnicas de factorizacin para operadores positivos. Adems, estudiamos la relacin entre los operadores estricta...

Tradacete Pe?rez, Pedro

2009-01-01

440

R-Orbit Reflexive Operators  

CERN Document Server

We completely characterize orbit reflexivity and R-orbit reflexivity for square matrices over the real numbers. Unlike the complex case in which every matrix is orbit reflexive and C-orbit reflexivity is characterized solely in terms of the Jordan form, the orbit reflexivity and R-orbit reflexivity of a real matrix is described in terms of the linear dependence over Q of certain elements of R/Q. We also show that every n-by-n matrix over an uncountable field F is algebraically F-orbit reflexive.

Hadwin, Don; Yousefi, Hassan

2011-01-01

 
 
 
 
441

Homotopical stable ranks for Banach algebras  

Digital Repository Infrastructure Vision for European Research (DRIVER)

The connected stable rank and the general stable rank are homotopy invariants for Banach algebras, whereas the Bass stable rank and the topological stable rank should be thought of as dimensional invariants. This paper studies the two homotopical stable ranks, viz. their general properties as well as specific examples and computations. The picture that emerges is that of a strong affinity between the homotopical stable ranks, and a marked contrast with the dimensional ones.

Nica, Bogdan

2009-01-01

442

Reflex sympathetic dystrophy  

International Nuclear Information System (INIS)

Reflex sympathetic dystrophy is characterized by intense and disproportionate local pain, associated with vasomotor and trophic changes. Extremities are commonly involved, especially when a trauma or surgery, even minor, has occurred. Likewise, spontaneous or idiopathic presentation of this syndrome is much less frequent. Here we describe the clinical picture of a young woman presenting with idiopathic reflex sympathetic dystrophy. Then we present a brief review, emphasizing on diagnosis and treatment of this disease.

2008-01-01

443

Supersets for the spectrum of elements in extended Banach algebras  

Directory of Open Access Journals (Sweden)

Full Text Available If A is a Banach Algebra with or without an identity, A can be always extended to a Banach algebra A¯ with identity, where A¯ is simply the direct sum of A and C, the algebra of complex numbers. In this note we find supersets for the spectrum of elements of A¯.

Morteza Seddighin

1989-09-01

444

On the Cauchy Functional Inequality in Banach Modules  

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We investigate the following functional inequality: ‖f(x)+f(y)+f(z)‖≤‖f(x+y+z)‖ in Banach modules over a C∗-algebra, and prove the generalized Hyers-Ulam stability of linear mappings in Banach modules over a C∗-algebra.

Choonkil Park

2008-01-01

445

Hyers-Ulam-Rassias stability of Jordan homomorphisms on Banach algebras  

Directory of Open Access Journals (Sweden)

Full Text Available We prove that a Jordan homomorphism from a Banach algebra into a semisimple commutative Banach algebra is a ring homomorphism. Using a signum effectively, we can give a simple proof of the Hyers-Ulam-Rassias stability of a Jordan homomorphism between Banach algebras. As a direct corollary, we show that to each approximate Jordan homomorphism from a Banach algebra into a semisimple commutative Banach algebra there corresponds a unique ring homomorphism near to .

Hirasawa Go

2005-01-01

446

On Reflection : Is Reflexivity Necessarily Beneficial in Intercultural Education?  

DEFF Research Database (Denmark)

This article explores how the concept of reflexivity is used in intercultural education. Reflexivity is often presented as a key learning goal in acquiring intercultural competence (ICC). Yet, reflexivity can be defined in different ways, and take different forms across time and space, depending on the concepts of selfhood that prevail and how notions of difference are constructed. First, I discuss how the dominant usages of reflexivity in intercultural education reflect and reproduce a Cartesian view of the self that shapes how ICC is conceptualized and taught. I discuss three assumptions that this view produces: that the self is accessible and transcendable, that reflexivity is universal across space and time, and that the self can act as its own remedial change agent or ??inner consultant.?? I argue that because reflexivity is understood in many different ways, attention to definition is crucial, both in designing learning objectives in intercultural education and in devising ways to attain them. Greater attention is also needed in intercultural education to the ways in which selfhood, and hence also reflexivity and constructions of difference, differ across space and time.

Blasco, Maribel

2012-01-01

447

Unconditional basic sequences in spaces of large density  

CERN Document Server

We study the problem of the existence of unconditional basic sequences in Banach spaces of high density. We show, in particular, the relative consistency with GCH of the statement that every Banach space of density $\\aleph_\\omega$ contains an unconditional basic sequence.

Dodos, Pandelis; Todorcevic, Stevo

2008-01-01

448

Spatial numerical ranges of elements of Banach algebras  

Directory of Open Access Journals (Sweden)

Full Text Available In this paper, the notion of spatial numerical range of elements of Banach algebras without identity is studied. Specifically, the relationship between spatial numerical ranges, numerical ranges and spectra is investigated. Among other results, it is shown that the closure of the spatial numerical range of an element of a Banach algebra without Identity but wlth regular norm is exactly its numerical range as an element of the unitized algebra. Futhermore, the closure of the spatial numerical range of a hermitian element coincides with the convex hull of its spectrum. In particular, spatial numerical ranges of the elements of the Banach algebra C0(X are described.

T. Husain

1989-09-01

449

Fixed points of cone compression and expansion multimaps defined on Frchet spaces: The projective limit approach  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We present a generalization of the cone compression and expansion results due to Krasnoselskii and Petryshyn for multivalued maps defined on a Frchet space E. The proof relies on fixed point results in Banach spaces and viewing E as the projective limit of a sequence of Banach spaces.

2006-01-01

450

A Banach algebraic Approach to the Borsuk-Ulam Theorem  

CERN Document Server

Using methods from the theory of commutative graded Banach algebras, we obtain a generalization of the two dimensional Borsuk-Ulam theorem as follows: Let $\\phi:S^{2} \\rightarrow S^{2}$ be a homeomorphism of order n and $\\lambda\

Taghavi, Ali

2011-01-01

451

Topological radicals, IV. Frattini theory for Banach Lie algebras  

CERN Document Server

The paper develops the theory of topological radicals of Banach Lie algebras and studies the structure of Banach Lie algebras with sufficiently many Lie subalgebras of finite codimensions -- the intersection of all these subalgebras is zero. It is shown that the intersections of certain families of Lie subalgebras (closed Lie subalgebras of finite codimension, closed Lie ideals of finite codimension, closed maximal Lie subalgebras of finite codimension, closed maximal Lie ideals of finite codimension) correspond to different preradicals, and that these preradicals generate the same radical, the Frattini radical. The main attention is given to structural properties of Frattini-semisimple Banach Lie algebras and, in particular, to a new infinite-dimensional phenomenon associated with the strong Frattini preradical introduced in this paper. A constructive description of Frattini-free Banach Lie algebras is obtained.

Kissin, Edward; Turovskii, Yurii

2012-01-01

452

Plongements des espaces mtriques dans les espaces de Banach.  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Le thme central de cette thse est le plongement des espaces mtriques dans les espaces de Banach. Les principaux plongements tudis sont les plongements grossiers, uniformes ou Lipschitziens. On considre des questions concernant le plongement Lipschitzien de certaines classes d'espaces mtriques, notamment les espaces mtriques localement finis ou plus gnralement les sous-ensembles localement finis des espaces de Banach Lp, avec 1<= p <= [infini]. Ces questions sont troiteme...

2009-01-01

453

Mazur spaces  

Directory of Open Access Journals (Sweden)

Full Text Available A Mazur space is a locally convex topological vector space X such that every fϵXs is continuous where Xs is the set of sequentially continuous linear functionals on X; Xs is studied when X is of the form C(H, H a topological space, and when X is the weak * dual of a locally convex space. This leads to a new classification of compact T2 spaces H, those for which the weak * dual of C(H is a Mazur space. An open question about Banach spaces with weak * sequentially compact dual ball is settled: the dual space need not be Mazur.

Albert Wilansky

1981-03-01

454

H reflex studies in neurolathyrism.  

Science.gov (United States)

Sixteen patients with lathyrism, age ranging between 18 and 55 years and duration of illness between 2 and 25 years, underwent H reflex studies with the aim of studying motor neurone excitability. The patients had marked spasticity (Ashworth score ranging between 2 and 5) and mild to moderate leg weakness. Knee and ankle reflexes were exaggerated in all and the plantar response was extensor in 14 patients. The H reflex abnormalities included increased HM ratio indicating increased motoneurone excitability, significant lack of vibratory inhibition indicating altered transmission in the premotoneuronal portion of the H reflex pathway, and lack of reciprocal inhibition (P < 0.01). These H reflex abnormalities were not related to spasticity, weakness, clonus or plantar response. The H reflex recovery curve in 6 patients revealed increased excitability throughout the recovery curve. The secondary facilitation started and peaked slightly earlier than normal, and the late depression was not marked indicating change in excitability of motoneurones or of interneurones. PMID:7521288

Misra, U K; Pandey, C M

1994-08-01

455

Analytic subsets of Hilbert spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We show that every complete metric space is homeomorphic to the precise locus of zeros of an entire analytic map from a Hilbert space to a Banach space. As a corollary, every complete separable metric space is homeomorphic to the precise locus of zeros of an entire analytic map between two separable complex Hilbert spaces. AmS TeX 2.1.

Pestov, Vladimir

1995-01-01

456

Reflex myoclonus in olivopontocerebellar atrophy.  

Digital Repository Infrastructure Vision for European Research (DRIVER)

The presence of reflex myoclonus in response to touching and pin-pricking the wrist or stretching the fingers and to photic stimulation was assessed in 24 patients with a presumed diagnosis of olivopontocerebellar atrophy (OPCA) and in 30 age matched control subjects. Reflex myoclonus to soma-esthetic stimulation was found in 23 patients and in none of the controls. Photic myoclonus was present in 12 patients and in none of the controls. Electrophysiological study of the reflex myoclonus show...

1994-01-01

457

Cauchy-Jensen additive mappings in quasi-Banach algebras and its applications  

Directory of Open Access Journals (Sweden)

Full Text Available In this paper, we prove the Hyers-Ulam stability of homomorphisms in quasi-Banach algebras and of generalized derivations on quasi-Banach algebras for the following Cauchy-Jensen additive mappings

Choonkil Park

2013-02-01

458

Fixed points of cone compression and expansion multimaps defined on Fréchet spaces: The projective limit approach  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We present a generalization of the cone compression and expansion results due to Krasnoselskii and Petryshyn for multivalued maps defined on a Fréchet space E. The proof relies on fixed point results in Banach spaces and viewing E as the projective limit of a sequence of Banach spaces.

2006-01-01

459

Mazur spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

A Mazur space is a locally convex topological vector space X such that every fϵXs is continuous where Xs is the set of sequentially continuous linear functionals on X; Xs is studied when X is of the form C(H), H a topological space, and when X is the weak * dual of a locally convex space. This leads to a new classification of compact T2 spaces H, those for which the weak * dual of C(H) is a Mazur space. An open question about Banach spaces with weak * sequentially compact dual ball...

1981-01-01

460

Uniqueness of the maximal ideal of the Banach algebra of bounded operators on $C([0,\\omega_1])$  

CERN Document Server

Let $\\omega_1$ be the first uncountable ordinal. By a result of Rudin, bounded operators on the Banach space $C([0,\\omega_1])$ have a natural representation as $[0,\\omega_1]\\times 0,\\omega_1]$-matrices. Loy and Willis observed that the set of operators whose final column is continuous when viewed as a scalar-valued function on $[0,\\omega_1]$ defines a maximal ideal of codimension one in the Banach algebra $\\mathscr{B}(C([0,\\omega_1]))$ of bounded operators on $C([0,\\omega_1])$. We give a coordinate-free characterization of this ideal and deduce from it that $\\mathscr{B}(C([0,\\omega_1]))$ contains no other maximal ideals. We then obtain a list of equivalent conditions describing the strictly smaller ideal of operators with separable range, and finally we investigate the structure of the lattice of all closed ideals of $\\mathscr{B}(C([0,\\omega_1]))$.

Kania, Tomasz

2011-01-01

 
 
 
 
461

Patterning of somatosympathetic reflexes  

Science.gov (United States)

In a previous study, we reported that vestibular nerve stimulation in the cat elicits a specific pattern of sympathetic nerve activation, such that responses are particularly large in the renal nerve. This patterning of vestibulosympathetic reflexes was the same in anesthetized and decerebrate preparations. In the present study, we report that inputs from skin and muscle also elicit a specific patterning of sympathetic outflow, which is distinct from that produced by vestibular stimulation. Renal, superior mesenteric, and lumbar colonic nerves respond most strongly to forelimb and hindlimb nerve stimulation (approximately 60% of maximal nerve activation), whereas external carotid and hypogastric nerves were least sensitive to these inputs (approximately 20% of maximal nerve activation). In contrast to vestibulosympathetic reflexes, the expression of responses to skin and muscle afferent activation differs in decerebrate and anesthetized animals. In baroreceptor-intact animals, somatosympathetic responses were strongly attenuated (to 150 mmHg. These findings demonstrate that different types of somatic inputs elicit specific patterns of sympathetic nerve activation, presumably generated through distinct neural circuits.

Kerman, I. A.; Yates, B. J.

1999-01-01

462

Th\\'eor\\`eme de division de Weierstrass sur un anneau de Banach. Application aux espaces de Berkovich sur Z  

CERN Document Server

Nous d\\'emontrons un th\\'eor\\`eme de division de Weierstrass pour les points rigides des fibres d'un espace de Berkovich affine X sur un anneau de Banach A et en tirons des informations sur la structure locale de X. Lorsque A est un corps valu\\'e complet, un anneau de valuation discr\\`ete ou un anneau d'entiers de corps de nombres, nous en d\\'eduisons qu'en tout point de X, la fibre du faisceau structural est un anneau local noeth\\'erien et r\\'egulier. Nous montrons \\'egalement que le faisceau structural est coh\\'erent. Nos m\\'ethodes traitent de fa\\c{c}on unifi\\'ee espaces complexes et p-adiques. Weierstrass division theorem over a Banach ring. Application to Berkovich spaces over Z. We prove a Weierstrass division theorem for the rigid points of the fibers of an affine Berkovich space X over a Banach ring A and use it to study the local structure of X. In case A is a valued field, a discrete valuation ring or the ring of integers of a number field, we deduce that the stalks of the structure sheaf of X are n...

Poineau, Jrme

2012-01-01

463

Reflexive sig is an argument  

Digital Repository Infrastructure Vision for European Research (DRIVER)

This paper argues that the simple reflexive pronoun sig is unambiguously a thematic argument in Icelandic. This is shown to be true not only of sig with naturally reflexive verbs but also of inherently reflexive sig. This view is mainly supported by two sets of facts: (i) that sig is impossible with verbs that fail to theta-mark their object (middles and anticausatives), and (ii) that case assignment ...

Jhannes Gsli Jnsson

2011-01-01

464

The vestibulosympathetic reflex in humans: neural interactions between cardiovascular reflexes  

Science.gov (United States)

1. Over the past 5 years, there has been emerging evidence that the vestibular system regulates sympathetic nerve activity in humans. We have studied this issue in humans by using head-down rotation (HDR) in the prone position. 2. These studies have clearly demonstrated increases in muscle sympathetic nerve activity (MSNA) and calf vascular resistance during HDR. These responses are mediated by engagement of the otolith organs and not the semicircular canals. 3. However, differential activation of sympathetic nerve activity has been observed during HDR. Unlike MSNA, skin sympathetic nerve activity does not increase with HDR. 4. Examination of the vestibulosympathetic reflex with other cardiovascular reflexes (i.e. barorereflexes and skeletal muscle reflexes) has shown an additive interaction for MSNA. 5. The additive interaction between the baroreflexes and vestibulosympathetic reflex suggests that the vestibular system may assist in defending against orthostatic challenges in humans by elevating MSNA beyond that of the baroreflexes. 6. In addition, the further increase in MSNA via otolith stimulation during isometric handgrip, when arterial pressure is elevated markedly, indicates that the vestibulosympathetic reflex is a powerful activator of MSNA and may contribute to blood pressure and flow regulation during dynamic exercise. 7. Future studies will help evaluate the importance of the vestibulosympathetic reflex in clinical conditions associated with orthostatic hypotension.

Ray, Chester A.; Monahan, Kevin D.

2002-01-01

465

Generalized covariation and extended Fukushima decompositions for Banach valued processes. Application to windows of Dirichlet processes  

CERN Document Server

This paper concerns a class of Banach valued processes which have finite quadratic variation. The notion introduced here generalizes the classical one, of M\\'etivier and Pellaumail which is quite restrictive. We make use of the notion of $\\chi$-covariation which is a generalized notion of covariation for processes with values in two Banach spaces $B_{1}$ and $B_{2}$. $\\chi$ refers to a suitable subspace of the dual of the projective tensor product of $B_{1}$ and $B_{2}$. We investigate some $C^{1}$ type transformations for various classes of stochastic processes admitting a $\\chi$-quadratic variation and related properties. If $\\X^1$ and $\\X^2$ admit a $\\chi$-covariation, $F^i: B_i \\rightarrow \\R$, $i = 1, 2$ are of class $C^1$ with some supplementary assumptions then the covariation of the real processes $F^1(\\X^1)$ and $F^2(\\X^2)$ exist. A detailed analysis will be devoted to the so-called window processes. Let $X$ be a real continuous process; the $C([-\\tau,0])$-valued process $X(\\cdot)$ defined by $X_t(y)...

Di Girolami, Cristina

2011-01-01

466

Almost Lie structures on an anchored Banach bundle  

CERN Multimedia

Under appropriate assumptions, we generalize the concept of linear almost Poisson struc- tures, almost Lie algebroids, almost differentials in the framework of Banach anchored bundles and the relation between these objects. We then obtain an adapted formalism for mechanical systems which is illustrated by the evolutionary problem of the "Hilbert snake"

Cabau, Patrick

2011-01-01

467

Gelfand theory for non-commutative Banach algebras  

CERN Multimedia

Let $A$ be a Banach algebra. We call a pair $(G, B)$ a Gelfand theory for $A$ if the following axioms are satisfied: (G 1) $B$ is a $C^\\ast$-algebra, and $G : A \\to B$ is a homomorphism; (G 2) the assignment $L \\mapsto G^{-1}(L)$ is a bijection between the sets of maximal modularleft ideals of $B$ and $A$, respectively; (G 3) for each maximal modular left ideal $L$ of $B$, the linear map $G_L : A / G^{-1}(L) \\to B /L $ induced by $B$ has dense range. The Gelfand theory of a commutative Banach algebra is easily seen to be characterized by these axioms. Gelfand theories of arbitrary Banach algebras enjoy many of the properties of commutative Gelfand theory. We show that unital, homogeneous Banach algebras always have a Gelfand theory. For liminal $C^\\ast$-algebras with discrete spectrum, we show that the identity is the only Gelfand theory (up to an appropriate notion of equivalence).

Choukri, R; Runde, V; Choukri, Rachid; Illoussamen, El Hossein; Runde, Volker

2002-01-01

468

Polynomial Bridgeland Stable Objects and Reflexive Sheaves  

CERN Document Server

On a smooth projective threefold, we show that there are only two isomorphism types for the moduli of stable objects with respect to Bayer's standard polynomial Bridgeland stability - the moduli of Gieseker-stable sheaves and the moduli of PT-stable objects - under the following assumptions: no two of the stability vectors are collinear, and the degree and rank of the objects are relatively prime. We also describe a close relation between the intersection of the moduli spaces of PT-stable and dual-PT-stable objects, and the moduli of reflexive sheaves.

Lo, Jason

2011-01-01

469

Geometry of Mntz spaces and related questions  

CERN Multimedia

Starting point and motivation for this volume is the classical Muentz theorem which states that the space of all polynomials on the unit interval, whose exponents have too many gaps, is no longer dense in the space of all continuous functions. The resulting spaces of Muentz polynomials are largely unexplored as far as the Banach space geometry is concerned and deserve the attention that the authors arouse. They present the known theorems and prove new results concerning, for example, the isomorphic and isometric classification and the existence of bases in these spaces. Moreover they state many open problems. Although the viewpoint is that of the geometry of Banach spaces they only assume that the reader is familiar with basic functional analysis. In the first part of the book the Banach spaces notions are systematically introduced and are later on applied for Muentz spaces. They include the opening and inclination of subspaces, bases and bounded approximation properties and versions of universality.

Gurariy, Vladimir

2005-01-01

470

Optimization in function spaces with stability considerations in Orlicz spaces  

CERN Document Server

This is an essentially self-contained book on the theory of convex functions and convex optimization in Banach spaces, with a special interest in Orlicz spaces. Approximate algorithms based on the stability principles and the solution of the corresponding nonlinear equationsaredeveloped in this text.A synopsis of the geometry of Banach spaces, aspects of stability and the duality of different levels of differentiability and convexity is developed. And it isprovided a novel approach to the fundamental theorems of Variational Calculus based on the principle of pointwise minimization of the Lagra

Kosmol, Peter

2011-01-01

471

On some fixed point theorems in Banach spaces  

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Full Text Available In this paper, some fixed point theorems are proved for multi-mappings as well as a pair of mappings. These extend certain known results due to Kirk, Browder, Kanna, Ćirić and Rhoades.

P. Veeramani

1982-03-01

472

On exponential stability of C_0-quasisemigroups in Banach spaces  

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Full Text Available Inthis paper we study some stability concepts for linear systems the evolution which can be described by a C_0 -quasisemigroup.The results obtained may be regarded as generalizations of well known results of Datko, Pazy, Littman and Neerven about exponential stability of C_0 -semigroups.

Mihail Megan

1999-10-01

473

Existence theorems for functional differential equations in Banach spaces  

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Full Text Available This paper concernes with the study of existence theorems for a general class of functional differential equations of the form u'(t=f(t,u circ g(t,cdot.The obtained results generalize the retarded functional differential equations [5], [6], [8] and cover singular functional differential equations [1], [3], [4], [7], [9], [12].

A. Sghir

2009-08-01

474

Characteristic exponents of impulsive differential equations in a Banach space  

International Nuclear Information System (INIS)

The notion of general exponent of impulsive homogeneous differential equations is defined. A formula for the solution of impulsive nonhomogeneous differential equations is obtained and is used to establish a dependence between the existence of bounded solutions of such equations and the general exponent of the respective homogeneous equation

1988-01-01

475

On isomorphisms and hyper-reflexivity of closed subspace lattices  

Digital Repository Infrastructure Vision for European Research (DRIVER)

There are some papers, such as [1], [2] and [3], in which some properties on isomorphism of closed subspace lattices of Hilbert spaces were studied. In this short paper we will point out that the hyper-reflexivity of closed subspace lattice is invariant under isomorphism of ξ(H1) on ξ(H2). We also proved that if T is in L(H) such that 0∈¯π(T) and ℱ is a hyper-reflexive subspace lattice, then ϕT(ℱ)∪{H} ...

Han Deguang

1991-01-01

476

Absolutely continuous functions with values in metric spaces  

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We present a general theory of absolutely continuous paths with values in metric spaces using the notion of metric derivatives. Among other results, we prove analogues of the Banach-Zarecki and Vallee Poussin theorems.

Duda, Jakub

2005-01-01

477

On isomorphisms and hyper-reflexivity of closed subspace lattices  

Directory of Open Access Journals (Sweden)

Full Text Available There are some papers, such as [1], [2] and [3], in which some properties on isomorphism of closed subspace lattices of Hilbert spaces were studied. In this short paper we will point out that the hyper-reflexivity of closed subspace lattice is invariant under isomorphism of ξ(H1 on ξ(H2. We also proved that if T is in L(H such that 0∈¯π(T and ℱ is a hyper-reflexive subspace lattice, then ϕT(ℱ∪{H} is hyper-reflexive where ϕT is a homomorphism induced by T.

Han Deguang

1991-09-01

478

Reflexive Dirinya: A Syntactic Analysis  

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Full Text Available This article discusses noun phrase (NP diriya which is known as reflexive in Malay language. However, this reflexive has an ambiguous reading in a sentence. This is because the NP dirinya can have a reference in a clause as well as outside a clause in the same sentence. As a result, this reflexive disobeyed Principle A. On the other hand, this type of reflexive occasionally is known as a long distance reflexive. Mashudi and Solakhiah (1997 had analysed this form of dirinya in a generative framework. They have claimed that the ambiguous reading of this reflexive dirinya was caused by the existence of [+reflexive] and [+pronominal] features which is generated by the NP dirinya at Sstructure. Even though, both of these language experts have argued very convincingly that the reason for the ambiguity of the NP dirinya was because of the different of features that existed on the NP but they didnt explain how two readings could have co-existed at the same level in the syntax. Their suggestions to have two readings to operate at the same level will not be able to reach the explanatory adequacy of a grammar. This analysis too will not be able to explain sentences like these: Sayai percaya bahawa Salimj telah menembak dirinya*i/j/k. (I believe that Salim has shot himself atau Salimj percaya bahawa sayai telah menembak dirinya*i/j/k.( Salim believe that I have shot himself/myself. Therefore, this paper will try to fill the gaps. This analysis claims that the reasons for the ambiguity is due to the features [+3] and [+pronominal] on the enclitic -nya and the feature [+reflexive] on the form diri which operates at a different syntactic level. This means that the ambiguity reading on dirinya in a sentence is because at the D-structure the native speaker will have the pronominal reading and it continues to exist until the Sstructure. At the S-structure, the speaker will have reflexive reading. The existence of two readings at different levels will cause dirinya to have an ambiguity reading. This analysis will be argued using the Binding Theory which controls the distribution of NP in a sentence.

Fazal Mohamed

2008-01-01

479

Capacitary function spaces and applications  

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The first part of the thesis is devoted to the analysis on a capacity space, with capacities as substitutes of measures in the study of function spaces. The goal is to extend to the associated function lattices some aspects of the theory of Banach function spaces, to show how the general theory can be applied to classical function spaces such as Lorentz spaces, and to complete the real interpolation theory for these spaces included in [CeClM] and [Ce].

Silvestre Albero, Mari?a Pilar

2012-01-01

480

Capacitary function spaces and applications  

Digital Repository Infrastructure Vision for European Research (DRIVER)

[eng] The first part of the thesis is devoted to the analysis on a capacity space, with capacities as substitutes of measures in the study of function spaces. The goal is to extend to the associated function lattices some aspects of the theory of Banach function spaces, to show how the general theory can be applied to classical function spaces such as Lorentz spaces, and to complete the real interpolation theory for these spaces included in [CeClM] and [Ce].

Silvestre Albero, Mari?a Pilar

2012-01-01

 
 
 
 
481

Reflexive algebras and sigma algebras  

Directory of Open Access Journals (Sweden)

Full Text Available The concept of a reflexive algebra (σ-algebra β of subsets of a set X is defined in this paper. Various characterizations are given for an algebra (σ-algebra β to be reflexive. If V is a real vector lattice of functions on a set X which is closed for pointwise limits of functions and if β={A|A⫅X   and   CA(x∈V} is the σ-algebra induced by V then necessary and sufficient conditions are given for β to be reflexive (where CA(x is the indicator function.

V. K. Srinivasan

1986-12-01

482

Sneeze reflex: facts and fiction.  

Science.gov (United States)

Sneezing is a protective reflex, and is sometimes a sign of various medical conditions. Sneezing has been a remarkable sign throughout the history. In Asia and Europe, superstitions regarding sneezing extend through a wide range of races and countries, and it has an ominous significance. Although sneezing is a protective reflex response, little else is known about it. A sneeze (or sternutation) is expulsion of air from the lungs through the nose and mouth, most commonly caused by the irritation of the nasal mucosa. Sneezing can further be triggered through sudden exposure to bright light, a particularly full stomach and physical stimulants of the trigeminal nerve, as a result of central nervous system pathologies such as epilepsy, posterior inferior cerebellar artery syndrome or as a symptom of psychogenic pathologies. In this first comprehensive review of the sneeze reflex in the English literature, we aim to review the pathophysiology, etiology, diagnosis, treatment and complications of sneezing. PMID:19617285

Songu, Murat; Cingi, Cemal

2009-06-01

483

On the Banach $*$-algebra crossed product associated with a topological dynamical system  

CERN Document Server

Given an arbitrary topological dynamical system $\\Sigma = (X, \\sigma)$, where $X$ is a compact Hausdorff space and $\\sigma$ a homeomorphism of $X$, we introduce and analyze the associated Banach $*$-algebra crossed product $\\ell^1 (\\Sigma)$. The $C^*$-envelope of this algebra is the usual $C^*$-crossed product of $C(X)$ by the integers under the automorphism of $C(X)$ induced by $\\sigma$. While the connections between the structure of this $C^*$-algebra and the properties of $\\Sigma$ are well-studied, such considerations concerning $\\ell^1 (\\Sigma)$ are new. We derive equivalences between topological dynamical properties of $\\Sigma$ and structural properties of $\\ell^1 (\\Sigma)$ that have well-known analogues in the $C^*$-algebra context, but also obtain a result on this so-called interplay whose counterpart in the case of $C^* (\\Sigma)$ is false.

Svensson, Christian

2009-01-01

484

Lectures given at the Banach Center and C.I.M.E. Joint Summer School  

CERN Document Server

The aim of this volume that presents Lectures given at a joint CIME and Banach Center Summer School, is to offer a broad presentation of a class of updated methods providing a mathematical framework for the development of a hierarchy of models of complex systems in the natural sciences, with a special attention to Biology and Medicine. Mastering complexity implies sharing different tools requiring much higher level of communication between different mathematical and scientific schools, for solving classes of problems of the same nature. Today more than ever, one of the most important challenges derives from the need to bridge parts of a system evolving at different time and space scales, especially with respect to computational affordability. As a result the content has a rather general character; the main role is played by stochastic processes, positive semigroups, asymptotic analysis, kinetic theory, continuum theory and game theory.

Lachowicz, Miros?aw

2008-01-01

485

How incomputable is the separable Hahn-Banach theorem?  

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We determine the computational complexity of the Hahn-Banach Extension Theorem. To do so, we investigate some basic connections between reverse mathematics and computable analysis. In particular, we use Weak Konig's Lemma within the framework of computable analysis to classify incomputable functions of low complexity. By defining the multi-valued function Sep and a natural notion of reducibility for multi-valued functions, we obtain a computational counterpart of the subsyst...

Gherardi, Guido; Marcone, Alberto

2008-01-01

486

Algebras of singular integral operators on nakano spaces with khvedelidze weights over carleson curves with logarithmic whirl points  

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We establish a Fredholm criterion for an arbitrary operator in the Banach algebra of singular integral operators with piecewise continuous coefficients on Nakano spaces (generalized Lebesgue spaces with variable exponent) with Khvedelidze weights over Carleson curves with logarithmic whirl points.

2005-01-01

487

The facial reflex of allergy.  

Science.gov (United States)

The facial reflex, originally described by Franz Chvostek, is shown to be of value in allergy by assessing the relative irritability of muscle tissue (cardic, smooth, skeletal) and the effect of certain drugs frequently used by allergists upon them. PMID:222174

Breneman, J C

1979-06-01

488

The fixed point property via dual space properties  

CERN Document Server

A Banach space has the weak fixed point property if its dual space has a weak$^*$ sequentially compact unit ball and the dual space satisfies the weak$^*$ uniform Kadec-Klee property; and it has the \\fpp if there exists $\\epsilon>0$ such that, for every infinite subset $A$ of the unit sphere of the dual space, $A\\cup (-A)$ fails to be $(2-\\epsilon)$-separated. In particular, $E$-convex Banach spaces, a class of spaces that includes the uniformly nonsquare spaces, have the fixed point property.

Dowling, P N; Turett, B

2008-01-01

489

Riemann-Stieltjes Operators between Vector-Valued Weighted Bloch Spaces  

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Full Text Available Let X be a Banach space, we study Riemann-Stieltjes operators between X-valued weighted Bloch spaces. Some necessary and sufficient conditions for these operators induced by holomorphic functions to be weakly compact and weakly conditionally compact are given by certain growth properties of the inducing symbols and some structural properties of the abstract Banach space, which extend some previous results.

Maofa Wang

2008-10-01

490

[Babkin's reflex in newborn: new reflexogenous zone].  

Science.gov (United States)

The authors have studied the hand-mouth reflex of Babkin on 422 newborns. 413 out of 422 newborns were considered normal. We have found responses not yet published such as accentuation of inferior limb flexion, trunk flexion, upper limb adduction, contraction of the mentalis muscle, contraction of the orbicular of the lips, extension of the inferior limb, extension of the pododactiles and cry. We obtained the same responses by pressing the infraclavicular space just near the esternal bone. We compared statistically: a) responses to the stimulus on the palm of the hand and on the new reflexogenous zone; b) responses presented by term and preterm newborns; c) responses of newborns less than 12 hours of age and more than 24 hours of age. PMID:14688951

Santos, G L; da Silva, A S; Novais, S L

1996-01-01

491

Modular functionals and perturbations of Nakano spaces  

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We settle several questions regarding the model theory of Nakano spaces left open by the PhD thesis of Pedro Poitevin \\cite{Poitevin:PhD}. We start by studying isometric Banach lattice embeddings of Nakano spaces, showing that in dimension two and above such embeddings have a particularly simple and rigid form. We use this to show show that in the Banach lattice language the modular functional is definable and that complete theories of atomless Nakano spaces are model complete. We also show t...

2009-01-01

492

Getting 'Entangled': Reflexivity and the 'Critical Turn' in Tourism Studies  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Reflecting a broader postmodern shift to unmask the cultural politics of research and knowledge-making in academia, tourism studies as a field is demonstrating a notable `critical turn a shift in thought that serves to provide and legitimise a space for more interpretative and critical modes of tourism inquiry. In response to this critical turn, this paper addresses the central issue of `reflexivity which, while alive in other disciplines and fields, has received rather limited attenti...

Ateljevic, I.; Harris, C.; Wilson, E.; Collins, F. L.

2005-01-01

493

Maximal abelian subalgebras and projections in two Banach algebras associated with a topological dynamical system  

CERN Multimedia

If $\\Sigma=(X,\\sigma)$ is a topological dynamical system, where $X$ is a compact Hausdorff space and $\\sigma$ is a homeomorphism of $X$, then a crossed product Banach $\\sp{*}$-algebra $\\ell^1(\\Sigma)$ is naturally associated with these data. If $X$ consists of one point, then $\\ell^1(\\Sigma)$ is the group algebra of the integers. The commutant $C(X)'_1$ of $C(X)$ in $\\ell^1(\\Sigma)$ is known to be a maximal abelian subalgebra which has non-zero intersection with each non-zero closed ideal, and the same holds for the commutant $C(X)'_*$ of $C(X)$ in $C^*(\\Sigma)$, the enveloping $C^*$-algebra of $\\ell^1(\\Sigma)$. This intersection property has proven to be a valuable tool in investigating these algebras. Motivated by this pivotal role, we study $C(X)'_1$ and $C(X)'_*$ in detail in the present paper. The maximal ideal space of $C(X)'_1$ is described explicitly, and is seen to coincide with its pure state space and to be a topological quotient of $X\\times\\mathbb{T}$. We show that $C(X)'_1$ is hermitian and semis...

de Jeu, Marcel

2011-01-01

494

Avaliao dos reflexos espinhais em bezerros Spinal reflexes in calves  

Directory of Open Access Journals (Sweden)

Full Text Available Este trabalho objetivou avaliar, quantificar e padronizar a ocorrncia dos reflexos espinhais em bezerros da raa holandesa de 15 a 90 dias de idade, os quais foram submetidos a avaliao nos membros torcicos (reflexo carpo radial, reflexo bicipital, reflexo tricipital e reflexo flexor e nos membros plvicos (reflexo patelar, reflexo tibial cranial, reflexo gastrocnmio, reflexo citico e reflexo flexor. Para quantificao da resposta involuntria frente ao reflexo realizado, padronizou-se a ausncia do reflexo como sendo o algarismo 0; resposta discreta do reflexo como sendo l e a presena evidente da resposta como sendo 2. Os reflexos mais evidentes e constantes foram os reflexos flexor, carpo radial, patelar e tricipital. Os reflexos menos evidentes e menos freqentes foram os reflexos tibial cranial, bicipital, gastrocnmio e citico.A study was carried out to evaluate the spinal reflexes of Holstein calves (15 to 90 days. Spinal reflexes were tested and graded (0 = absence, I = mild reflex, 2 = evident in thoracic (extensor carpi reflex, biceps reflex, triceps reflex and flexor reflex and pelvic (patellar reflex, cranial tibial reflex, gastrocnemius reflex, ciatic reflex and flexor reflex limbs. The flexor reflex, extensor carpi reflex, patellar and triceps reflex were elicited in most animals. While the least evident reflexes were, cranial tibial reflex, biceps reflex, gastrocnemius reflex and ciatic reflex.

Alexandre Secorun Borges

1997-12-01

495

The passive of reflexive verbs in Icelandic  

Digital Repository Infrastructure Vision for European Research (DRIVER)

The Reflexive Passive in Icelandic is reminiscent of the so-called New Passive (or New Impersonal) in that the oblique case of a passivized object NP is preserved. As is shown by recent surveys, however, speakers who accept the Reflexive Passive do not necessarily accept the New Passive, whereas conversely, speakers who accept the New Passive do also accept the Reflexive Passive. Based on these results we suggest that there is a hierarchy in the acceptance of passive sentences in Icelandic, t...

Hlf rnadttir; Thrhallur Eythrsson; Einar Freyr Sigursson

2011-01-01

496

Pelczynski's property (V) on spaces of vector valued functions  

CERN Document Server

Let $E$ be a separable Banach space and $\\Omega$ be a compact Hausdorff space. It is shown that the space $C(\\Omega,E)$ has property (V) if and only if $E$ does. Similar result is also given for Bochner spaces $L^p(\\mu,E)$ if $1

Randrianantoanina, N

1994-01-01

497

Superstability for Generalized Module Left Derivations and Generalized Module Derivations on a Banach Module (I  

Directory of Open Access Journals (Sweden)

Full Text Available We discuss the superstability of generalized module left derivations and generalized module derivations on a Banach module. Let be a Banach algebra and a Banach -module, and . The mappings , and are defined and it is proved that if (resp., is dominated by then is a generalized (resp., linear module- left derivation and is a (resp., linear module- left derivation. It is also shown that if (resp., is dominated by then is a generalized (resp., linear module- derivation and is a (resp., linear module- derivation.

Rassias JM

2009-01-01

498

Stable Ranks, K-Groups and Witt Groups of some Banach and C-star Algebras  

CERN Document Server

We show that certain dense and spectral invariant subalgebras of a $C^*$-algebra have the same bilateral Bass stable rank. This is a partial answer for (a version of) an open problem raised by R.G. Swan. Then, for certain Banach algebras, we indicate when the homotopy groups result due to G. Corach and A. Larotonda. Using some results due to M. Karoubi, we show the isomorphism of the Witt group of a symmetric Banach algebra with the $K_0$-group of its enveloping $C^*$-algebra. The question if this is true for all involutive Banach algebras was raised by A. Connes.

Badea, C

1999-01-01

499

Superstability for Generalized Module Left Derivations and Generalized Module Derivations on a Banach Module (I)  

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We discuss the superstability of generalized module left derivations and generalized module derivations on a Banach module. Let 𝒜 be a Banach algebra and X a Banach 𝒜-module, f:X?X and g:𝒜?𝒜. The mappings ?f,g1,??f,g2,??f,g3, and ?f,g4 are defined and it is proved that if ??f,g1(x,y,z,w)? (resp., ??f,g3(x,y,z,w,?,?)?) is dominated by ?(x,y,z,w...

2009-01-01

500

21 CFR 890.1450 - Powered reflex hammer.  

Science.gov (United States)

...2010-04-01 2010-04-01 false Powered reflex hammer. 890.1450 Section 890.1450...Diagnostic Devices § 890.1450 Powered reflex hammer. (a) Identification. A powered reflex hammer is a motorized device intended...

2010-04-01