The cofinal property of the Reflexive Indecomposable Banach spaces
Argyros, Spiros A; Raikoftsalis, Theocharis
2010-01-01
It is shown that every separable reflexive Banach space is a quotient of a reflexive Hereditarily Indecomposable space, which yields that every separable reflexive Banach is isomorphic to a subspace of a reflexive Indecomposable space. Furthermore, every separable reflexive Banach space is a quotient of a reflexive complementably $\\ell_p$ saturated space with $1
Rigidity of commuting affine actions on reflexive Banach spaces
Rosendal, Christian
2012-01-01
We give a simple argument to show that if {\\alpha} is an affine isometric action of a product G x H of topological groups on a reflexive Banach space X with linear part {\\pi}, then either {\\pi}(H) fixes a unit vector or {\\alpha}|G almost fixes a point on X. It follows that any affine isometric action of an abelian group on a reflexive Banach space X, whose linear part fixes no unit vectors, almost fixes points on X.
On J. Borwein's concept of sequentially reflexive Banach spaces
Ørno, Peter
1991-01-01
A Banach space $X$ is reflexive if the Mackey topology $\\tau(X^*,X)$ on $X^*$ agrees with the norm topology on $X^*$. Borwein [B] calls a Banach space $X$ {\\it sequentially reflexive\\/} provided that every $\\tau(X^*,X)$ convergent {\\it sequence\\/} in $X^*$ is norm convergent. The main result in [B] is that $X$ is sequentially reflexive if every separable subspace of $X$ has separable dual, and Borwein asks for a characterization of sequentially reflexive spaces. Here we answer that question b...
Metrical characterization of super-reflexivity and linear type of Banach spaces
Baudier, Florent
2007-01-01
We prove that a Banach space X is not super-reflexive if and only if the hyperbolic infinite tree embeds metrically into X. We improve one implication of J.Bourgain's result who gave a metrical characterization of super-reflexivity in Banach spaces in terms of uniforms embeddings of the finite trees. A characterization of the linear type for Banach spaces is given using the embedding of the infinite tree equipped with a suitable metric.
First and Second Order Convex Sweeping Processes in Reflexive Smooth Banach Spaces
In this paper we establish new characterizations of the normal cone of closed convex sets in reflexive smooth Banach spaces and then we use those results to prove the existence of solutions for first order convex sweeping processes and their variants in reflexive smooth Banach spaces. The case of second order convex sweeping processes is also studied. (author)
Some fixed point theorems in fuzzy reflexive Banach spaces
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 α- 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.
Composite iterative schemes for maximal monotone operators in reflexive Banach spaces
Cho Yeol
2011-01-01
Full Text Available Abstract In this article, we introduce composite iterative schemes for finding a zero point of a finite family of maximal monotone operators in a reflexive Banach space. Then, we prove strong convergence theorems by using a shrinking projection method. Moreover, we also apply our results to a system of convex minimization problems in reflexive Banach spaces. AMS Subject Classification: 47H09, 47H10
On solvability of general nonlinear variational-like inequalities in reflexive Banach spaces
Soo Hak Shim
2005-07-01
Full Text Available We introduce and study a new class of general nonlinear variational-like inequalities in reflexive Banach spaces. By applying a minimax inequality, we establish two existence and uniqueness theorems of solutions for the general nonlinear variational-like inequality.
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 { λn} be a sequence in (0, 1) satisfying the following conditions: C1 : lim λn 0; C2 : Σ λn = ∞ . For a fixed δ element of (0, 1), define Sn : K → K by Snx := (1 - δ )x + δTnx 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 γx+(1- γ)u, for some γ > 1} be bounded and let the sequence {xn} be defined iteratively by xn+1 λn+1u + (1 - λn+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)
Casazza, Peter G.; Lammers, Mark C.
1999-01-01
We show that the classification problem for genus $n$ Banach spaces can be reduced to the unconditionally primary case and that the critical case there is $n=2$. It is further shown that a genus $n$ Banach space is unconditionally primary if and only if it contains a complemented subspace of genus $(n-1)$. We begin the process of classifying the genus 2 spaces by showing they have a strong decomposition property.
Topological duals of Banach spaces as Banach algebras and applications
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
Multipliers of Banach valued weighted function spaces
Serap Öztop
2000-10-01
Full Text Available 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.
Separably injective Banach spaces
Avilés, Antonio; Castillo, Jesús M F; González, Manuel; Moreno, Yolanda
2016-01-01
This monograph contains a detailed exposition of the up-to-date theory of separably injective spaces: new and old results are put into perspective with concrete examples (such as l∞/c0 and C(K) spaces, where K is a finite height compact space or an F-space, ultrapowers of L∞ spaces and spaces of universal disposition). It is no exaggeration to say that the theory of separably injective Banach spaces is strikingly different from that of injective spaces. For instance, separably injective Banach spaces are not necessarily isometric to, or complemented subspaces of, spaces of continuous functions on a compact space. Moreover, in contrast to the scarcity of examples and general results concerning injective spaces, we know of many different types of separably injective spaces and there is a rich theory around them. The monograph is completed with a preparatory chapter on injective spaces, a chapter on higher cardinal versions of separable injectivity and a lively discussion of open problems and further lines o...
On asymptotic models in Banach spaces
Halbeisen, Lorenz; Odell, Edward
2001-01-01
A well known application of Ramsey's Theorem to Banach Space Theory is the notion of a spreading model (e'_i) of a normalized basic sequence (x_i) in a Banach space X. We show how to generalize the construction to define a new creature (e_i), which we call an asymptotic model of X. Every spreading model of X is an asymptotic model of X and in most settings, such as if X is reflexive, every normalized block basis of an asymptotic model is itself an asymptotic model. We also show how to use the...
Adjoint Operators on Banach Spaces
Gill, Tepper L; Zachary, Woodford W
2010-01-01
In this paper, we report on new results related to the existence of an adjoint for operators on separable Banach spaces and discuss a few interesting applications. (Some results are new even for Hilbert spaces.) Our first two applications provide an extension of the Poincar\\'{e} inequality and the Stone-von Neumann version of the spectral theorem for a large class of $C_0$-generators of contraction semigroups on separable Banach spaces. Our third application provides a natural extension of the Schatten-class of operators to all separable Banach spaces. As a part of this program, we introduce a new class of separable Banach spaces. As a side benefit, these spaces also provide a natural framework for the (rigorous) construction of the path integral as envisioned by Feynman.
A pythagorean approach in Banach spaces
Gao Ji
2006-01-01
Let be a Banach space and let be the unit sphere of . Parameters , , , and , where and are introduced and studied. The values of these parameters in the spaces and function spaces are estimated. Among the other results, we proved that a Banach space with , or is uniform nonsquare; and a Banach space with , or has uniform normal structure.
Fusion Frames and -Frames in Banach Spaces
Amir Khosravi; Behrooz Khosravi
2011-05-01
Fusion frames and -frames in Hilbert spaces are generalizations of frames, and frames were extended to Banach spaces. In this article we introduce fusion frames, -frames, Banach -frames in Banach spaces and we show that they share many useful properties with their corresponding notions in Hilbert spaces. We also show that -frames, fusion frames and Banach -frames are stable under small perturbations and invertible operators.
Smooth analysis in Banach spaces
Hjek, Petr
2014-01-01
This bookis aboutthe subject of higher smoothness in separable real Banach spaces.It brings together several angles of view on polynomials, both in finite and infinite setting.Also a rather thorough and systematic view of the more recent results, and the authors work is given. The book revolves around two main broad questions: What is the best smoothness of a given Banach space, and its structural consequences? How large is a supply of smooth functions in the sense of approximating continuous functions in the uniform topology, i.e. how does the Stone-Weierstrass theorem generalize into in
Characterizing R-duality in Banach spaces
Christensen, Ole; Xiao, Xiang Chun; Zhu, Yu Can
2013-01-01
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.......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....
Existence of zeros for operators taking their values in the dual of a Banach space
Ricceri Biagio
2004-01-01
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.
On factorization of operators between Banach spaces
Tokarev, Eugene
2002-01-01
A finite-dimensional analogue of the known Gordon-Lewis constant of a Banach space X is introduced; in its definition are used only finite rank operators. It is shown that there exist Banach spaces such that the standard Gordon-Lewis constant of X is finite and its finite-dimensional analogue GLfin(X) is infinite. Moreover, for any Banach space X of cotype 2 its finite-dimensional constant GLfin(X) is finite too.
Isometries on Banach spaces function spaces
Fleming, Richard J
2002-01-01
Fundamental to the study of any mathematical structure is an understanding of its symmetries. In the class of Banach spaces, this leads naturally to a study of isometries-the linear transformations that preserve distances. In his foundational treatise, Banach showed that every linear isometry on the space of continuous functions on a compact metric space must transform a continuous function x into a continuous function y satisfying y(t) = h(t)x(p(t)), where p is a homeomorphism and |h| is identically one.Isometries on Banach Spaces: Function Spaces is the first of two planned volumes that survey investigations of Banach-space isometries. This volume emphasizes the characterization of isometries and focuses on establishing the type of explicit, canonical form given above in a variety of settings. After an introductory discussion of isometries in general, four chapters are devoted to describing the isometries on classical function spaces. The final chapter explores isometries on Banach algebras.This treatment p...
Regularization methods in Banach spaces
Schuster, Thomas; Hofmann, Bernd; Kazimierski, Kamil S
2012-01-01
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
Compactness in Banach space theory - selected problems
Avilés, Antonio; Kalenda, Ondřej F. K.
2010-01-01
We list a number of problems in several topics related to compactness in nonseparable Banach spaces. Namely, about the Hilbertian ball in its weak topology, spaces of continuous functions on Eberlein compacta, WCG Banach spaces, Valdivia compacta and Radon-Nikod\\'{y}m compacta.
Banach spaces of analytic functions
Hoffman, Kenneth
2007-01-01
A classic of pure mathematics, this advanced graduate-level text explores the intersection of functional analysis and analytic function theory. Close in spirit to abstract harmonic analysis, it is confined to Banach spaces of analytic functions in the unit disc.The author devotes the first four chapters to proofs of classical theorems on boundary values and boundary integral representations of analytic functions in the unit disc, including generalizations to Dirichlet algebras. The fifth chapter contains the factorization theory of Hp functions, a discussion of some partial extensions of the f
Coefficient Quantization for Frames in Banach Spaces
Casazza, P. G.; Dilworth, S. J.; Odell, E.; Schlumprecht, Th.; Zsak, Andras
2007-01-01
Let $(e_i)$ be a fundamental system of a Banach space. We consider the problem of approximating linear combinations of elements of this system by linear combinations using quantized coefficients. We will concentrate on systems which are possibly redundant. Our model for this situation will be frames in Banach spaces.
Geometry of Banach spaces and biorthogonal systems
Dilworth, S. J.; Girardi, Maria; Johnson, W. B.
1999-01-01
A separable Banach space X contains $\\ell_1$ isomorphically if and only if X has a bounded wc_0^*-stable biorthogonal system. The dual of a separable Banach space X fails the Schur property if and only if X has a bounded wc_0^*-biorthogonal system.
Simultaneous approximation in scales of Banach spaces
The problem of verifying optimal approximation simultaneously in different norms in a Banach scale is reduced to verification of optimal approximation in the highest order norm. The basic tool used is the Banach space interpolation method developed by Lions and Peetre. Applications are given to several problems arising in the theory of finite element methods
On Uniformly finitely extensible Banach spaces
Castillo, Jesús M. F.; Ferenczi, Valentin; Moreno, Yolanda
2013-01-01
We continue the study of Uniformly Finitely Extensible Banach spaces (in short, UFO) initiated in Moreno-Plichko, \\emph{On automorphic Banach spaces}, Israel J. Math. 169 (2009) 29--45 and Castillo-Plichko, \\emph{Banach spaces in various positions.} J. Funct. Anal. 259 (2010) 2098-2138. We show that they have the Uniform Approximation Property of Pe\\l czy\\'nski and Rosenthal and are compactly extensible. We will also consider their connection with the automorphic space problem of Lindenstraus...
Condensation rank of injective Banach spaces
Gazor, Majid
2011-01-01
The condensation rank associates any topological space with a unique ordinal number. In this paper we prove that the condensation rank of any infinite dimensional injective Banach space is equal to or greater than the first uncountable ordinal number.
Isometric embeddings of compact spaces into Banach spaces
Dutrieux, Yves; Lancien, Gilles
2008-01-01
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 $X$ is a polyhedral fi...
On Λ-Type Duality of Frames in Banach Spaces
Renu Chugh
2013-11-01
Full Text Available Frames are redundant system which are useful in the reconstruction of certain classes of spaces. The dual of a frame (Hilbert always exists and can be obtained in a natural way. Due to the presence of three Banach spaces in the definition of retro Banach frames (or Banach frames duality of frames in Banach spaces is not similar to frames for Hilbert spaces. In this paper we introduce the notion of Λ-type duality of retro Banach frames. This can be generalized to Banach frames in Banach spaces. Necessary and sufficient conditions for the existence of the dual of retro Banach frames are obtained. A special class of retro Banach frames which always admit a dual frame is discussed.
A Gaussian Average Property for Banach Spaces
Casazza, Peter G.; Nielsen, Niels Jorgen
1996-01-01
In this paper we investigate a Gaussian average property of Banach spaces. This property is weaker than the Gordon Lewis property but closely related to this and other unconditional structures. It is also shown that this property implies that certain Hilbert space valued operators defined on subspaces of the given space can be extended.
On Sharp Triangle Inequalities in Banach Spaces II
Kichi-Suke Saito
2010-01-01
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.
On Banach spaces without the approximation property
Reinov, Oleg I.
2002-01-01
A. Szankowski's example is used to construct a Banach space similar to that of "An example of an asymptotically Hilbertian space which fails the approximation property", P.G. Casazza, C.L. Garc\\'{\\i}a, W.B. Johnson [math.FA/0006134 ()].
Completely positive linear operators for Banach spaces
Mingze Yang
1994-03-01
Full Text Available Using ideas of Pisier, the concept of complete positivity is generalized in a different direction in this paper, where the Hilbert space Ã¢Â„Â‹ is replaced with a Banach space and its conjugate linear dual. The extreme point results of Arveson are reformulated in this more general setting.
Quantitative Hahn-Banach Theorems and Isometric Extensions for Wavelet and Other Banach Spaces
Sergey Ajiev
2013-01-01
We introduce and study Clarkson, Dolnikov-Pichugov, Jacobi and mutual diameter constants reflecting the geometry of a Banach space and Clarkson, Jacobi and Pichugov classes of Banach spaces and their relations with James, self-Jung, Kottman and Schffer constants in order to establish quantitative versions of Hahn-Banach separability theorem and to characterise the isometric extendability of Hlder-Lipschitz mappings. Abstract results are further applied to the spaces and pairs from the wide...
Boundary Controllability of Integrodifferential Systems in Banach Spaces
K Balachandran; E R Anandhi
2001-02-01
Sufficient conditions for boundary controllability of integrodifferential systems in Banach spaces are established. The results are obtained by using the strongly continuous semigroup theory and the Banach contraction principle. Examples are provided to illustrate the theory.
Discretization of variational regularization in Banach spaces
Poeschl, C; Scherzer, O
2010-01-01
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.
Nonlinear evolution equations on Banach space
Ahmed, N.U.
1991-01-01
In this paper we consider the questions of existence and uniqueness of solutions of certain semilinear and quasilinear evolution equations on Banach space. We consider both deterministic and stochastic systems. The approach is based on semigroup theory and fixed point theorems. Our results allow the nonlinear perturbations in all the semilinear problems to be bounded or unbounded with reference to the base space, thereby increasing the scope for applications to partial differential equations....
Fixed point theorems for generalized Lipschitzian semigroups in Banach spaces
Jong Soo Jung
1999-03-01
Full Text Available Fixed point theorems for generalized Lipschitzian semigroups are proved in p-uniformly convex Banach spaces and in uniformly convex Banach spaces. As applications, its corollaries are given in a Hilbert space, in Lp spaces, in Hardy space Hp, and in Sobolev spaces Hk,p, for 1
p-representable operators in Banach spaces
Roshdi Khalil
1986-12-01
Full Text Available Let E and F be Banach spaces. An operator TâL(E,F is called p-representable if there exists a finite measure Î¼ on the unit ball, B(E*, of E* and a function gâLq(Î¼,F, 1p+1q=1, such thatTx=â«B(E*â©x,x*âªg(x*dÎ¼(x*for all xâE. The object of this paper is to investigate the class of all p-representable operators. In particular, it is shown that p-representable operators form a Banach ideal which is stable under injective tensor product. A characterization via factorization through Lp-spaces is given.
Boundedness of biorthogonal systems in Banach spaces
Hájek, Petr Pavel; Montesinos, V.
2010-01-01
Roč. 177, č. 1 (2010), s. 145-154. ISSN 0021-2172 R&D Projects: GA ČR GA201/07/0394 Institutional research plan: CEZ:AV0Z10190503 Keywords : M-basis * Banach spaces Subject RIV: BA - General Mathematics Impact factor: 0.630, year: 2010 http://link.springer.com/article/10.1007%2Fs11856-010-0041-x
Topological Vector-Space Valued Cone Banach Spaces
Nayyar Mehmood; Akbar Azam; Suzana Aleksic
2014-01-01
In this paper we introduce the notion of tvs-cone normed spaces, discuss related topological concepts and characterize the tvs-cone norm in various directions. We construct generalize locally convex tvs generated by a family of tvs-cone seminorms. The class of weak contractions properly includes large classes of highly applicable contractions like Banach, Kannan, Chatterjea and quasi etc. We prove fixed point results in tvs-cone Banach spaces for nonexpansive self mappings and self/non-self w...
Characterization of Banach valued BMO functions and UMD Banach spaces by using Bessel convolutions
Betancor, Jorge J; Rodríguez-Mesa, Lourdes
2011-01-01
In this paper we consider the space $BMO_o(\\mathbb{R},X)$ of bounded mean oscillations and odd functions on $\\mathbb{R}$ taking values in a UMD Banach space $X$. The functions in $BMO_o(\\mathbb{R},X)$ are characterized by Carleson type conditions involving Bessel convolutions and $\\gamma$-radonifying norms. Also we prove that the UMD Banach spaces are the unique Banach spaces for which certain $\\gamma$-radonifying Carleson inequalities for Bessel-Poisson integrals of $BMO_o(\\mathbb{R},X)$ functions hold.
The Diameter of the Isomorphism Class of a Banach Space
Johnson, W. B.; Odell, E.
2003-01-01
We prove that if X is a separable infinite dimensional Banach space then its isomorphism class has infinite diameter with respect to the Banach-Mazur distance. One step in the proof is to show that if X is elastic then X contains an isomorph of c_0. We call X elastic if for some K < infinity for every Banach space Y which embeds into X, the space Y is K-isomorphic to a subspace of X. We also prove that if X is a separable Banach space such that for some K < infinity every isomorph of X is K-e...
Introduction to Banach spaces and algebras
Allan, Graham
2010-01-01
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
Some results concerning frames in Banach spaces
S. K. Kaushik
2007-01-01
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 ret...
Frame Wavelet Sets and Wavelets in Banach Spaces
Devendra Kumar
2014-06-01
Full Text Available In this paper, we try to study a special class of frame wavelets in Banach spaces whose Fourier transforms are supported by frame wavelet sets. Our results generalize the various results of [2] to Banach spaces other than Hilbert spaces using the Feichtinger and Grochenig theory.
Discretization of variational regularization in Banach spaces
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
Discretization of variational regularization in Banach spaces
Pschl, Christiane; Resmerita, Elena; Scherzer, Otmar
2010-10-01
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.
Impulsive integral equations in Banach spaces and applications
Dajun Guo
1992-01-01
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.
Unbounded operators on Banach spaces over the quaternion field
Ludkovsky, S. V.
2004-01-01
Resolvents of quasi-linear operators and operator algebras in Banach spaces over the quaternion field are investigated. Spectral theory of unbounded nonlinear operators in quaternion Banach spaces is studied. Strongly continuous semigroups of quaternion quasi-linear operators are investigated and the polar decomposition theorem for them is proved.
Nonlinear impulsive Volterra integral equations in Banach spaces and applications
Dajun Guo
1993-01-01
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.
Minimal and Maximal Operator Space Structures on Banach Spaces
P., Vinod Kumar; Balasubramani, M. S.
2014-01-01
Given a Banach space $X$, there are many operator space structures possible on $X$, which all have $X$ as their first matrix level. Blecher and Paulsen identified two extreme operator space structures on $X$, namely $Min(X)$ and $Max(X)$ which represents respectively, the smallest and the largest operator space structures admissible on $X$. In this note, we consider the subspace and the quotient space structure of minimal and maximal operator spaces.
Amenability for dual Banach algebras
Runde, Volker
2002-01-01
We define a Banach algebra A to be dual if $A = (A_\\ast)^\\ast$ for a closed submodule $A_\\ast$ of $A^\\ast$. The class of dual Banach algebras includes all $W^\\ast$-algebras, but also all algebras M(G) for locally compact groups G, all algebras L(E) for reflexive Banach spaces E, as well as all biduals of Arens regular Banach algebras. The general impression is that amenable, dual Banach algebras are rather the exception than the rule. We confirm this impression. We first show that under certa...
BANACH CONTRACTION PRINCIPLE ON CONE RECTANGULAR METRIC SPACES
Ismat Beg
2009-08-01
Full Text Available We introduce the notion of cone rectangular metric space and prove {sc Banach} contraction mapping principle in cone rectangular metric space setting. Our result extends recent known results.
On Shrinking and Boundedly Complete Schauder Frames of Banach spaces
Liu, Rui
2009-01-01
This paper studies Schauder frames in Banach spaces, a concept which is a natural generalization of frames in Hilbert spaces and Schauder bases in Banach spaces. The associated minimal and maximal spaces are introduced, as are shrinking and boundedly complete Schauder frames. Our main results extend the classical duality theorems on bases to the situation of Schauder frames. In particular, we will generalize James' results on shrinking and boundedly complete bases to frames. Secondly we will ...
Convergence on Composite Iterative Schemes for Nonexpansive Mappings in Banach Spaces
Jong Soo Jung
2008-01-01
Abstract Let be a reflexive Banach space with a uniformly Gâteaux 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 s...
On nested sequences of convex sets in a Banach space
Castillo, Jesús M. F.; González, Manuel; Papini, Pier Luigi
2014-01-01
In this paper we study different aspects of the representation of weak*-compact convex sets of the bidual $X^{**}$ of a separable Banach space $X$ via a nested sequence of closed convex bounded sets of $X$.
Some Questions Arising from the Homogeneous Banach Space Problem
Casazza, Peter G.
1992-01-01
We review the current state of the homogeneous Banach space problem. We then formulate several questions which arise naturally from this problem, some of which seem to be fundamental but new. We give many examples defining the bounds on the problem. We end with a simple construction showing that every infinite dimensional Banach space contains a subspace on which weak properties have become stable (under passing to further subspaces). Implications of this construction are considered.
Banach spaces with many boundedly complete basic sequences failing PCP
Perez, Gines Lopez
2009-01-01
We prove that there exist Banach spaces not containing $\\ell_1$, failing the point of continuity property and satisfying that every semi-normalized basic sequence has a boundedly complete basic subsequence. This answers in the negative the problem of the Remark 2 in H. P. Rosenthal. "Boundedly complete weak-Cauchy sequences in Banach spaces with PCP." J. Funct. Anal. 253 (2007) 772-781.
Quantitative Hahn-Banach Theorems and Isometric Extensions forWavelet and Other Banach Spaces
Sergey Ajiev
2013-05-01
Full Text Available We introduce and study Clarkson, Dolnikov-Pichugov, Jacobi and mutual diameter constants reflecting the geometry of a Banach space and Clarkson, Jacobi and Pichugov classes of Banach spaces and their relations with James, self-Jung, Kottman and Schffer constants in order to establish quantitative versions of Hahn-Banach separability theorem and to characterise the isometric extendability of Hlder-Lipschitz mappings. Abstract results are further applied to the spaces and pairs from the wide classes IG and IG+ and non-commutative Lp-spaces. The intimate relation between the subspaces and quotients of the IG-spaces on one side and various types of anisotropic Besov, Lizorkin-Triebel and Sobolev spaces of functions on open subsets of an Euclidean space defined in terms of differences, local polynomial approximations, wavelet decompositions and other means (as well as the duals and the lp-sums of all these spaces on the other side, allows us to present the algorithm of extending the main results of the article to the latter spaces and pairs. Special attention is paid to the matter of sharpness. Our approach is quasi-Euclidean in its nature because it relies on the extrapolation of properties of Hilbert spaces and the study of 1-complemented subspaces of the spaces under consideration.
On the Bounded Approximation Property in Banach spaces
Castillo, Jesús M. F.; Moreno, Yolanda
2013-01-01
We prove that the kernel of a quotient operator from an $\\mathcal L_1$-space onto a Banach space $X$ with the Bounded Approximation Property (BAP) has the BAP. This completes earlier results of Lusky --case $\\ell_1$-- and Figiel, Johnson and Pe\\l czy\\'nski --case $X^*$ separable. Given a Banach space $X$, we show that if the kernel of a quotient map from some $\\mathcal L_1$-space onto $X$ has the BAP then every kernel of every quotient map from any $\\mathcal L_1$-space onto $X$ has the BAP. T...
Banach frames for multivariate alpha-modulation spaces
Borup, Lasse; Nielsen, Morten
2006-01-01
The ?-modulation spaces [$Mathematical Term$], form a family of spaces that include the Besov and modulation spaces as special cases. This paper is concerned with construction of Banach frames for ?-modulation spaces in the multivariate setting. The frames constructed are unions of independent...
Construction of generalized atomic decompositions in Banach spaces
Raj Kumar
2014-06-01
Full Text Available G-atomic decompositions for Banach spaces with respect to a model space of sequences have been introduced and studied as a generalization of atomic decompositions. Examples and counter example have been provided to show its existence. It has been proved that an associated Banach space for G-atomic decomposition always has a complemented subspace. The notion of a representation system is introduced and exhibits its relation with G-atomic decomposition. Also It has been observed that G-atomic decompositions are exactly compressions of Schauder decompositions for a larger Banach space. We give a characterization for finite G-atomic decomposition in terms of finite-dimensional expansion of identity. Keywords: complemented coefficient spaces, finite-dimensional expansion of identity, G-atomic decomposition, representation system.
Tauberian theorems for generalized functions with values in Banach spaces
We state and prove Tauberian theorems of a new type. In these theorems we give sufficient conditions under which the values of a generalized function (distribution) that are assumed to lie in a locally convex topological space actually belong to some narrower (Banach) space. These conditions are stated in terms of 'general class estimates' for the standard average of this generalized function with a fixed kernel belonging to a space of test functions. The applications of these theorems are based, in particular, on the fact that asymptotical (and some other) properties of the generalized functions under investigation can be described in terms of membership of certain Banach spaces. We apply these theorems to the study of asymptotic properties of solutions of the Cauchy problem for the heat equation in the class of generalized functions of small growth (tempered distributions), and to the study of Banach spaces of Besov-Nikol'skii type
Tauberian theorems for generalized functions with values in Banach spaces
Drozhzhinov, Yu N; Zav' yalov, B I [Steklov Mathematical Institute, Russian Academy of Sciences (Russian Federation)
2002-08-31
We state and prove Tauberian theorems of a new type. In these theorems we give sufficient conditions under which the values of a generalized function (distribution) that are assumed to lie in a locally convex topological space actually belong to some narrower (Banach) space. These conditions are stated in terms of 'general class estimates' for the standard average of this generalized function with a fixed kernel belonging to a space of test functions. The applications of these theorems are based, in particular, on the fact that asymptotical (and some other) properties of the generalized functions under investigation can be described in terms of membership of certain Banach spaces. We apply these theorems to the study of asymptotic properties of solutions of the Cauchy problem for the heat equation in the class of generalized functions of small growth (tempered distributions), and to the study of Banach spaces of Besov-Nikol'skii type.
Reproducing Kernel Banach Spaces with the l1 Norm
Song, Guohui; Hickernell, Fred J
2011-01-01
Targeting at sparse learning, we construct Banach spaces B of functions on an input space X with the properties that (1) B possesses an l1 norm in the sense that it is isometrically isomorphic to the Banach space of integrable functions on X with respect to the counting measure; (2) point evaluations are continuous linear functionals on B and are representable through a bilinear form with a kernel function; (3) regularized learning schemes on B satisfy the linear representer theorem. Examples of kernel functions admissible for the construction of such spaces are given.
Metric embeddings bilipschitz and coarse embeddings into Banach spaces
Ostrovskii, Mikhail I
2013-01-01
Embeddings of discrete metric spaces into Banach spaces recently became an important tool in computer science and topology. The book will help readers to enter and to work in this very rapidly developing area having many important connections with different parts of mathematics and computer science. The purpose of the book is to present some of the most important techniques and results, mostly on bilipschitz and coarse embeddings. The topics include embeddability of locally finite metric spaces into Banach spaces is finitely determined, constructions of embeddings, distortion in terms of Poinc
Semigroups preserving a convex set in a Banach space
Shigekawa, Ichiro
2011-01-01
We discuss semigroups that preserve a convex set in a Banach space or a Hilbert space. We give sufficient conditions for which a semigroup preserves a convex set. Using this, we show that various issues can be treated in a unified way. We also discuss the problem in the Hilbert space setting, in which we use the sesquilinear form associated with a semigroup.
Banach's space: Lviv and the Scottish cafe
Henderson, D.
2004-01-01
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.
Banach's space: Lviv and the Scottish cafe
D.Henderson
2004-01-01
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.
A GLIDING HUMP PROPERTY AND BANACH-MACKEY SPACES
CHARLES SWARTZ
2001-08-01
Full Text Available We consider the Banach-Mackey property for pairs of vector spaces E and E' which are in duality. Let A be an algebra of sets and assume that P is an additive map from A into the projection operators on E. We define a continuous gliding hump property for the map P and show that pairs with this gliding hump property and anoter measure theoretic property are Banach-Mackey pairs, i. e., weakly bounded subsets of E are strongly bounded. Examples of vector valued function spaces, such as the space of Pettis integrable functions, which satisfy these conditions are given
Banach spaces and groups - order properties and universal models
Shelah, S; Shelah, Saharon; Usvyatsov, Alex
2003-01-01
We deal with two natural examples of almost-elementary classes: the class of all Banach spaces (over R or C) and the class of all groups. We show both of these classes do not have the strict order property, and find the exact place of each one of them in Shelah's SOP_n (strong order property of order n) hierarchy. Remembering the connection between this hierarchy and the existence of universal models, we conclude, for example, that there are ``few'' universal Banach spaces (under isometry) of regular cardinalities.
Riesz Isomorphisms of Tensor Products of Order Unit Banach Spaces
T S S R K Rao
2009-06-01
In this paper we formulate and prove an order unit Banach space version of a Banach–Stone theorem type theorem for Riesz isomorphisms of the space of vector-valued continuous functions. Similar results were obtained recently for the case of lattice-valued continuous functions in [5] and [6].
Total subspaces in dual Banach spaces which are not norming
Ostrovskii, Mikhail I.
1993-01-01
The main result: the dual of separable Banach space $X$ contains a total subspace which is not norming over any infinite dimensional subspace of $X$ if and only if $X$ has a nonquasireflexive quotient space with the strictly singular quotient mapping.
The reconstruction property in Banach spaces and a perturbation theorem
Casazza, P.G.; Christensen, Ole
2008-01-01
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 equiva...
Smooth approximations of norms in separable Banach spaces
Hájek, Petr Pavel; Talponen, J.
2014-01-01
Roč. 65, č. 3 (2014), s. 957-969. ISSN 0033-5606 R&D Projects: GA ČR(CZ) GAP201/11/0345 Institutional support: RVO:67985840 Keywords : Banach space * approximation Subject RIV: BA - General Mathematics Impact factor: 0.640, year: 2014 http://qjmath.oxfordjournals.org/content/65/3/957
On polynomial equations in Banach space, perturbation techniques and applications
Ioannis K. Argyros
1987-03-01
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.
A characterization of Banach space with non expansive map
In this paper, we characterize a Banach space X with a certain non expansive map T: X → X. We shall prove that T is non expansive if and only if each three dimensional subspace of X has the property that, after rotation by π/2, its unit ball coincides with its dual unit ball. (authors). 3 refs
The M-basis Problem for Separable Banach Spaces
Gill, Tepper L.
2013-01-01
In this note we show that, if $\\mcB$ is separable Banach space, then there is a biorthogonal system $\\{x_n, x_n^*\\}$ such that, the closed linear span of $\\{x_n\\},\\bar{\\left\\langle {\\{x_n\\}}\\right\\rangle}=\\mcB$ and $\\left\\| {x_n} \\right\\|\\left\\| {x_n^*} \\right\\| = 1$ for all $n$.
On some impulsive fractional differential equations in Banach spaces
JinRong Wang
2010-01-01
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.
On the Weak Relatively Nonexpansive Mappings in Banach Spaces
Yongfu Su
2010-01-01
Full Text Available In recent years, the definition of weak relatively nonexpansive mapping has been presented and studied by many authors. In this paper, we give some results about weak relatively nonexpansive mappings and give two examples which are weak relatively nonexpansive mappings but not relatively nonexpansive mappings in Banach space l2 and Lp[0,1]? ?(1
On the Weak Relatively Nonexpansive Mappings in Banach Spaces
Su Yongfu
2010-01-01
Full Text Available Abstract In recent years, the definition of weak relatively nonexpansive mapping has been presented and studied by many authors. In this paper, we give some results about weak relatively nonexpansive mappings and give two examples which are weak relatively nonexpansive mappings but not relatively nonexpansive mappings in Banach space and .
Fast regularizing sequential subspace optimization in Banach spaces
We are concerned with fast computations of regularized solutions of linear operator equations in Banach spaces in case only noisy data are available. To this end we modify recently developed sequential subspace optimization methods in such a way that the therein employed Bregman projections onto hyperplanes are replaced by Bregman projections onto stripes whose width is in the order of the noise level
Convergence on Composite Iterative Schemes for Nonexpansive Mappings in Banach Spaces
Jung JongSoo
2008-01-01
Full Text Available Abstract Let be a reflexive Banach space with a uniformly Gâteaux 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.
Iterative Approximation to Convex Feasibility Problems in Banach Space
Shih-Sen Chang
2007-04-01
Full Text Available The convex feasibility problem (CFP of finding a point in the nonempty intersection Ã¢ÂˆÂ©i=1NCi is considered, where NÃ¢Â‰Â¥1 is an integer and each Ci is assumed to be the fixed point set of a nonexpansive mapping Ti:EÃ¢Â†Â’E, where E is a reflexive Banach space with a weakly sequentially continuous duality mapping. By using viscosity approximation methods for a finite family of nonexpansive mappings, it is shown that for any given contractive mapping f:CÃ¢Â†Â’C, where C is a nonempty closed convex subset of E and for any given x0Ã¢ÂˆÂˆC the iterative scheme xn+1=P[ÃŽÂ±n+1f(xn+(1Ã¢ÂˆÂ’ÃŽÂ±n+1Tn+1xn] is strongly convergent to a solution of (CFP, if and only if {ÃŽÂ±n} and {xn} satisfy certain conditions, where ÃŽÂ±nÃ¢ÂˆÂˆ(0,1,Tn=Tn(modN and P is a sunny nonexpansive retraction of E onto C. The results presented in the paper extend and improve some recent results in Xu (2004, O'Hara et al. (2003, Song and Chen (2006, Bauschke (1996, Browder (1967, Halpern (1967, Jung (2005, Lions (1977, Moudafi (2000, Reich (1980, Wittmann (1992, Reich (1994.
Quantitative coarse embeddings of quasi-Banach spaces into a Hilbert space
Kraus, Michal
2015-01-01
We study how well a quasi-Banach space can be coarsely embedded into a Hilbert space. Given any quasi-Banach space X which coarsely embeds into a Hilbert space, we compute its Hilbert space compression exponent. We also show that the Hilbert space compression exponent of X is equal to the supremum of the amounts of snowflakings of X which admit a bi-Lipschitz embedding into a Hilbert space.
Embeddings of groups into Banach spaces
Jolissaint, Pierre-Nicolas; Valette, Alain
2015-01-01
L'objectif de cette thèse est de faire des liens entre les propriétés algébriques et géométriques des groupes. Une façon d'étudier un espace métrique quelconque est de le représenter comme un sous-ensemble d'un espace de Banach dont la géométrie est bien comprise. En premier lieu, nous étudions les plongements bi-Lipschitz de graphes de Cayley de groupes finis dans les espaces Lp [0; 1]. En particulier, nous donnons une borne inferieure pour la distortion de tels plongements à l'aide d'invari...
Integral operators on the section space of a Banach bundle
D. A. Robbins
1993-09-01
Full Text Available Let Ï:EâX and Ï:FâX be bundles of Banach spaces, where X is a compact Hausdorff space, and let V be a Banach space. Let Î(Ï denote the space of sections of the bundle Ï. We obtain two representations of integral operators T:Î(ÏâV in terms of measures. The first generalizes a recent result of P. Saab, the second generalizes a theorem of Grothendieck. We also study integral operators T:Î(ÏâÎ(Ï which are C(X-linear.
Integrals and Banach spaces for finite order distributions
Talvila, Erik
2011-01-01
Let $\\Bc$ denote the real-valued functions continuous on the extended real line and vanishing at $-\\infty$. Let $\\Br$ denote the functions that are left continuous, have a right limit at each point and vanish at $-\\infty$. Define $\\acn$ to be the space of tempered distributions that are the $n$th distributional derivative of a unique function in $\\Bc$. Similarly with $\\arn$ from $\\Br$. A type of integral is defined on distributions in $\\acn$ and $\\arn$. The multipliers are iterated integrals of functions of bounded variation. For each $n\\in\\N$, the spaces $\\acn$ and $\\arn$ are Banach spaces, Banach lattices and Banach algebras isometrically isomorphic to $\\Bc$ and $\\Br$, respectively. Under the ordering in this lattice, if a distribution is integrable then its absolute value is integrable. The dual space is isometrically isomorphic to the functions of bounded variation. The space $\\ac^1$ is the completion of the $L^1$ functions in the Alexiewicz norm. The space $\\ar^1$ contains all finite signed Borel measure...
On best proximity points in metric and Banach spaces
Espinola, Rafa
2009-01-01
In this paper we study the existence and uniqueness of best proximity points of cyclic contractions as well as the convergence of iterates to such proximity points. We do it from two different approaches, leading each one of them to different results which complete, if not improve, other similar results in the theory. Results in this paper stand for Banach spaces, geodesic metric spaces and metric spaces. We also include an appendix on CAT(0) spaces where we study the particular behavior of these spaces regarding the problems we are concerned with.
Some problems on ordinary differential equations in Banach spaces
Hájek, Petr Pavel; Vivi, P.
2010-01-01
Roč. 104, č. 2 (2010), s. 245-255. ISSN 1578-7303 R&D Projects: GA AV ČR IAA100190801; GA ČR GA201/07/0394 Institutional research plan: CEZ:AV0Z10190503 Keywords : Banach space * ODE * Peano's theorem Subject RIV: BA - General Mathematics Impact factor: 0.400, year: 2010 http://link.springer.com/article/10.5052%2FRACSAM.2010.16
Polynomial algebras and smooth functions in Banach spaces
D'Alessandro, Stefania; Hájek, Petr Pavel
2014-01-01
Roč. 266, č. 3 (2014), s. 1627-1646. ISSN 0022-1236 R&D Projects: GA ČR(CZ) GAP201/11/0345; GA MŠk(CZ) 7AMB12FR003 Institutional support: RVO:67985840 Keywords : polynomials in Banach space Subject RIV: BA - General Mathematics Impact factor: 1.322, year: 2014 http://www.sciencedirect.com/science/article/pii/S0022123613004588
Weak compactness and sigma-Asplund generated Banach spaces
Fabian, Marián; Montesinos, V.; Zizler, Václav
2007-01-01
Roč. 181, č. 2 (2007), s. 125-152. ISSN 0039-3223 R&D Projects: GA AV ČR IAA1019301; GA AV ČR(CZ) IAA100190610 Institutional research plan: CEZ:AV0Z10190503 Keywords : epsilon-Asplund set * epsilon-weakly compact set * weakly compactly generated Banach space Subject RIV: BA - General Mathematics Impact factor: 0.568, year: 2007
Elements of mathematical theory of evolutionary equations in Banach spaces
Samoilenko, Anatoly M
2013-01-01
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
A proximal point method for nonsmooth convex optimization problems in Banach spaces
Y. I. Alber
1997-01-01
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.
Greedy Algorithms for Reduced Bases in Banach Spaces
DeVore, Ronald
2013-02-26
Given a Banach space X and one of its compact sets F, we consider the problem of finding a good n-dimensional space X n⊂X which can be used to approximate the elements of F. The best possible error we can achieve for such an approximation is given by the Kolmogorov width dn(F)X. However, finding the space which gives this performance is typically numerically intractable. Recently, a new greedy strategy for obtaining good spaces was given in the context of the reduced basis method for solving a parametric family of PDEs. The performance of this greedy algorithm was initially analyzed in Buffa et al. (Modél. Math. Anal. Numér. 46:595-603, 2012) in the case X=H is a Hilbert space. The results of Buffa et al. (Modél. Math. Anal. Numér. 46:595-603, 2012) were significantly improved upon in Binev et al. (SIAM J. Math. Anal. 43:1457-1472, 2011). The purpose of the present paper is to give a new analysis of the performance of such greedy algorithms. Our analysis not only gives improved results for the Hilbert space case but can also be applied to the same greedy procedure in general Banach spaces. © 2013 Springer Science+Business Media New York.
A remark on contraction semigroups on Banach spaces
Lin, P K
1994-01-01
Let $X$ be a complex Banach space and let $J:X \\to X^*$ be a duality section on $X$ (i.e. $\\langle x,J(x)\\rangle=\\|J(x)\\|\\|x\\|=\\|J(x)\\|^2=\\|x\\|^2$). For any unit vector $x$ and any ($C_0$) contraction semigroup $T=\\{e^{tA}:t \\geq 0\\}$, Goldstein proved that if $X$ is a Hilbert space and if $|\\langle T(t) x,J(x)\\rangle| \\to 1 $ as $t \\to \\infty$, then $x$ is an eigenvector of $A$ corresponding to a purely imaginary eigenvalue. In this article, we prove the similar result holds if $X$ is a stri...
On moduli of convexity in Banach spaces
Reif Jiří
2005-01-01
Let be a normed linear space, an element of norm one, and and the local modulus of convexity of . We denote by the greatest such that for each closed linear subspace of the quotient mapping maps the open -neighbourhood of in onto a set containing the open -neighbourhood of in . It is known that . We prove that there is no universal constant such that , however, such a constant exists within the class of Hilbert spaces . If is a Hilbert space with , then .
On moduli of convexity in Banach spaces
Reif Jiří
2005-01-01
Full Text Available Let be a normed linear space, an element of norm one, and and the local modulus of convexity of . We denote by the greatest such that for each closed linear subspace of the quotient mapping maps the open -neighbourhood of in onto a set containing the open -neighbourhood of in . It is known that . We prove that there is no universal constant such that , however, such a constant exists within the class of Hilbert spaces . If is a Hilbert space with , then .
p-adic Banach space operators and adelic Banach space operators
Ilwoo Cho
2014-01-01
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.
Geometry and Gâteaux smoothness in separable Banach spaces
Hájek, Petr Pavel; Montesinos, V.; Zizler, Václav
2012-01-01
Roč. 6, č. 2 (2012), s. 201-232. ISSN 1846-3886 R&D Projects: GA ČR(CZ) GAP201/11/0345; GA AV ČR IAA100190901 Institutional research plan: CEZ:AV0Z10190503 Keywords : Gâteaux differentiable norms * extreme points * Radon-Nikodým property Subject RIV: BA - General Math ematics Impact factor: 0.529, year: 2012 http://oam.ele- math .com/06-15/Geometry-and-Gateaux-smoothness-in-separable-Banach-spaces
Weakly convex and proximally smooth sets in Banach spaces
We establish interconnections between the conditions of weak convexity in the sense of Vial, weak convexity in the sense of Efimov-Stechkin, and proximal smoothness of sets in Banach spaces. We prove a theorem on the separation by a sphere of two disjoint sets, one of which is weakly convex in the sense of Vial and the other is strongly convex. We also prove that weakly convex and proximally smooth sets are locally connected, and study questions related to the preservation of the conditions of weak convexity and proximal smoothness under passage to the limit
On nonautonomous second-order differential equations on Banach space
Nguyen Thanh Lan
2001-04-01
Full Text Available We show the existence and uniqueness of classical solutions of the nonautonomous second-order equation: uÃ¢Â€Â³(t=A(tuÃ¢Â€Â²(t+B(tu(t+f(t, 0Ã¢Â‰Â¤tÃ¢Â‰Â¤T; u(0=x0, uÃ¢Â€Â²(0=x1 on a Banach space by means of operator matrix method and apply to Volterra integrodifferential equations.
Smoothness in Banach spaces. Selected problems
Fabian, Marián; Montesinos, V.; Zizler, Václav
2006-01-01
Roč. 100, č. 2 (2006), s. 101-125. ISSN 1578-7303 R&D Projects: GA ČR(CZ) GA201/04/0090; GA AV ČR(CZ) IAA100190610 Institutional research plan: CEZ:AV0Z10190503 Keywords : smooth norm * renorming * weakly compactly generated space Subject RIV: BA - General Mathematics
This paper is concerned with chaotification of a class of discrete dynamical systems in Banach spaces via the feedback control technique. A chaotification theorem based on heteroclinic cycles connecting repellers for maps in Banach spaces is established. The controlled system is proved to be chaotic in the sense of both Devaney and Li-Yorke. An illustrative example is provided with computer simulations.
Numerical analysis of semilinear stochastic evolution equations in Banach spaces
Hausenblas, Erika
2002-10-01
The solution of stochastic evolution equations generally relies on numerical computation. Here, usually the main idea is to discretize the SPDE spatially obtaining a system of SDEs that can be solved by e.g., the Euler scheme. In this paper, we investigate the discretization error of semilinear stochastic evolution equations in Lp-spaces, resp. Banach spaces. The space discretization may be done by Galerkin approximation, for the time discretization we consider the implicit Euler, the explicit Euler scheme and the Crank-Nicholson scheme. In the last section, we give some examples, i.e., we consider an SPDEs driven by nuclear Wiener noise approximated by wavelets and delay equation approximated by finite differences.
Homomorphisms and functional calculus on algebras on entire functions on Banach spaces
H. M. Pryimak
2015-07-01
Full Text Available The paper is devoted to study homomorphisms of algebras of entire functionson Banach spaces to a commutative Banach algebra. In particular, it is proposed amethod to construct homomorphisms vanishing on homogeneouspolynomials of degree less or equal that a fixed number $n.$
Arunkumar, M
2013-01-01
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.
Stochastic integration in Banach spaces theory and applications
Mandrekar, Vidyadhar
2015-01-01
Considering Poisson random measures as the driving sources for stochastic (partial) differential equations allows us to incorporate jumps and to model sudden, unexpected phenomena. By using such equations the present book introduces a new method for modeling the states of complex systems perturbed by random sources over time, such as interest rates in financial markets or temperature distributions in a specific region. It studies properties of the solutions of the stochastic equations, observing the long-term behavior and the sensitivity of the solutions to changes in the initial data. The authors consider an integration theory of measurable and adapted processes in appropriate Banach spaces as well as the non-Gaussian case, whereas most of the literature only focuses on predictable settings in Hilbert spaces. The book is intended for graduate students and researchers in stochastic (partial) differential equations, mathematical finance and non-linear filtering and assumes a knowledge of the required integrati...
Frechet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces
Lindenstrauss, Joram; Tiaer, Jaroslav
2012-01-01
This book makes a significant inroad into the unexpectedly difficult question of existence of Fréchet 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
An Inversion Formula for the Gaussian Radon Transform for Banach Spaces
Holmes, Irina
2013-01-01
We provide a disintegration theorem for the Gaussian Radon transform Gf on Banach spaces and use the Segal-Bargmann transform on abstract Wiener spaces to find a procedure to obtain f from its Gaussian Radon transform Gf.
Kim JongKyu
2009-01-01
Full Text Available We study the strong convergence of two kinds of viscosity iteration processes for approximating common fixed points of the pseudocontractive semigroup in uniformly convex Banach spaces with uniformly Gteaux differential norms. As special cases, we get the strong convergence of the implicit viscosity iteration process for approximating common fixed points of the nonexpansive semigroup in Banach spaces satisfying some conditions. The results presented in this paper extend and generalize some results concerned with the nonexpansive semigroup in (Chen and He, 2007 and the pseudocontractive mapping in (Zegeye et al., 2007 to the pseudocontractive semigroup in Banach spaces under different conditions.
Parameter choice in Banach space regularization under variational inequalities
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)
Porous sets for mutually nearest points in Banach spaces
Chong Li
2008-01-01
Full Text Available Let \\(\\mathfrak{B}(X\\ denote the family of all nonempty closed bounded subsets of a real Banach space \\(X\\, endowed with the Hausdorff metric. For \\(E, F \\in \\mathfrak{B}(X\\ we set \\(\\lambda_{EF} = \\inf \\{\\|z - x\\| : x \\in E, z \\in F \\}\\. Let \\(\\mathfrak{D}\\ denote the closure (under the maximum distance of the set of all \\((E, F \\in \\mathfrak{B}(X \\times \\mathfrak{B}(X\\ such that \\(\\lambda_{EF} \\gt 0\\. It is proved that the set of all \\((E, F \\in \\mathfrak{D}\\ for which the minimization problem \\(\\min_{x \\in E, z\\in F}\\|x - z\\|\\ fails to be well posed in a \\(\\sigma\\-porous subset of \\(\\mathfrak{D}\\.
In this work, we establish a sufficient condition for the controllability of the first-order impulsive neutral functional differential inclusions with infinite delay in Banach spaces. The results are obtained by using the Dhage's fixed point theorem.
On Property () in Banach Lattices, Calderón–Lozanowskiĭ and Orlicz–Lorentz Spaces
Paweł Kolwicz
2001-08-01
The geometry of Calderón–Lozanowskiĭ spaces, which are strongly connected with the interpolation theory, was essentially developing during the last few years (see [4, 9, 10, 12, 13, 17]). On the other hand many authors investigated property () in Banach spaces (see [7, 19, 20, 21, 25, 26]). The first aim of this paper is to study property () in Banach function lattices. Namely a criterion for property () in Banach function lattice is presented. In particular we get that in Banach function lattice property () implies uniform monotonicity. Moreover, property () in generalized Calderón–Lozanowskiĭ function spaces is studied. Finally, it is shown that in Orlicz–Lorentz function spaces property () and uniform convexity coincide.
Initial value problems for integro-differential equations of Volterra type in Banach spaces
Dajun Guo
1994-01-01
Full Text Available This paper investigates the extremal solutions of initial value problems for first order integro-differential equations of Volterra type in Banach spaces by means of establishing a comparison result.
Approximating zero points of accretive operators with compact domains in general Banach spaces
Miyake Hiromichi
2005-01-01
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.
Ishikawa iteration process with errors for nonexpansive mappings in uniformly convex Banach spaces
Li Shenghong
2000-07-01
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.
Fourier transform of function on locally compact Abelian groups taking value in Banach spaces
Radyna, Yauhen; Sidorik, Anna
2008-01-01
We consider Fourier transform of vector-valued functions on a locally compact group $G$, which take value in a Banach space $X$, and are square-integrable in Bochner sense. If $G$ is a finite group then Fourier transform is a bounded operator. If $G$ is an infinite group then Fourier transform $F: L_2(G,X)\\to L_2(\\widehat G,X)$ is a bounded operator if and only if Banach space $X$ is isomorphic to a Hilbert one.
Approximation of Common Fixed Points for Families of Mappings in Banach Space
Zhiming Cheng
2012-06-01
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.
Diffeomorphisms between spheres and hyperplanes in infinite-dimensional Banach spaces
Azagra Rueda, Daniel
1997-01-01
We prove that for every infinite-dimensional Banach space X with a Frechet differentiable norm, the sphere S-X is diffeomorphic to each closed hyperplane in X. We also prove that every infinite-dimensional Banach space Y having a (not necessarily equivalent) C-p norm (with p is an element of N boolean OR {infinity}) is C-p diffeomorphic to Y \\ {0}.
Strong convergence theorems for uniformly L-Lipschitzian mappings in Banach spaces
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 {αn}n≥0 and {γn}n≥0 subset of (0, 1) be such that limn→∞ αn = 0 = limn→ ∞ γn and limn→ ∞(βn - 1)/ αn = 0, where βn Σj=0n λj and λj = 1 + αjγjL. Let Sn := (1 - αnγn)I + αnγnTn. 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 = αnu+(1 -αn) 1/ (n + 1) Σj=0n Sjxn. If φ : E → R is defined by φ (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 : φ (x) = min (u element of K) φ (u) }, then it is proved that {xn} converges strongly to a fixed point of T. As an application, it is proved that the iterative process, z0 element of K, zn+1 alpha#nu + (1 - αn) 1/ (n + 1) Σj=0n Sjzn , n ≥ 0, under suitable conditions on the iteration parameters, converges strongly to a fixed point of T. (author)
On the fixed point property in direct sums of Banach spaces with strictly monotone norms
Prus, Stanis?aw; Wi?nicki, Andrzej
2007-01-01
It is shown that if a Banach space X has the weak Banach-Saks property and the weak fixed point property for nonexpansive mappings and Y satisfies property asymptotic (P) (which is weaker than the condition WCS(Y)>1), then the direct sum of X and Y endowed with a strictly monotone norm enjoys the weak fixed point property. The same conclusion is valid if X admits a 1-unconditional basis.
Isometric uniqueness of a complementably universal Banach space for Schauder decompositions
Garbulińska, Joanna
2014-01-01
We present an isometric version of the complementably universal Banach space $\\mathbb{P}$ with a Schauder decomposition. The space $\\mathbb{P}$ is isomorphic to Pe{\\l}czy\\'nski's space with a universal basis as well as to Kadec' complementably universal space with the bounded approximation property.
Skipped Blocking and other Decompositions in Banach spaces
Bellenot, S F
2004-01-01
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.
Arens Regularity Of Bilinear Forms And Unital Banach Module Spaces
Azar, Kazem Haghnejad
2010-01-01
Assume that $A$, $B$ are Banach algebras and $m:A\\times B\\to B$, $m^\\prime:A\\times A\\to B$ are bounded bilinear mappings. We will study the relation between Arens regularities of $m$, $m^\\prime$ and the Banach algebras $A$, $B$. For Banach $A-bimodule$ $B$, we show that $B$ factors with respect to $A$ if and only if $B^{**}$ is an unital $A^{**}-module$, and we define locally topological center for elements of $A^{**}$ and will show that when locally topological center of mixed unit of $A^{**}$ is $B^{**}$, then $B^*$ factors on both sides with respect to $A$ if and only if $B^{**}$ has a unit as $A^{**}-module$.
Accretive operators and Banach Alaoglu theorem in Linear 2-normed spaces
P. K Harikrishnan; Bernardo La Fuerza Guilln; K. T Ravindran
2011-01-01
In this paper we introduce the concept of accretive operator in linear 2-normed spaces, focusing on the relationships and the various aspects of accretive, m-accretive and maximal accretive operators. We prove the analogous of Banach-Alaoglu theorem in linear 2- normed spaces, obtaining an equivalent definition for accretive operators in linear 2-normed spaces.
Fixed Point Theorems for an Elastic Nonlinear Mapping in Banach Spaces
Hiroko Manaka
2014-01-01
Let $E$ be a smooth Banach space with a norm $‖·‖$ . Let $V(x,y)={‖x‖}^{2}+{‖y‖}^{2}-2{\\langle}x,Jy{\\rangle}$ for any $x,y\\in E$ , where ${\\langle}·,·{\\rangle}$ stands for the duality pair and $J$ is the normalized duality mapping. We define a $V$ -strongly nonexpansive mapping by $V(·,·)$ . This nonlinear mapping is nonexpansive in a Hilbert space. However, we show that there exists a $V$ -strongly nonexpansive mapping with fixed points which is not nonexpansive in a Banach space. In this pa...
Nonstationary iterated Tikhonov regularization for ill-posed problems in Banach spaces
Jin, Qinian; Stals, Linda
2012-10-01
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.
Periodic and almost periodic solutions for multi-valued differential equations in Banach spaces
E. Hanebaly
2000-03-01
Full Text Available It is known that for $omega$-periodic differential equations of monotonous type, in uniformly convex Banach spaces, the existence of a bounded solution on ${Bbb R}^+$ is equivalent to the existence of an omega-periodic solution (see Haraux [5] and Hanebaly [7, 10]. It is also known that if the Banach space is strictly convex and the equation is almost periodic and of monotonous type, then the existence of a continuous solution with a precompact range is equivalent to the existence of an almost periodic solution (see Hanebaly [8]. In this note we want to generalize the results above for multi-valued differential equations.
Iterative approximation of a solution of a general variational-like inclusion in Banach spaces
In this paper, we introduce a class of η-accretive mappings in a real Banach space, and show that the η-proximal point mapping for η-m-accretive mapping is Lipschitz continuous. Further we develop an iterative algorithm for a class of general variational-like inclusions involving η-accretive mappings in real Banach space, and discuss its convergence criteria. The class of η-accretive mappings includes several important classes of operators that have been studied by various authors. (author)
A New Two-Step Iterative Process with Errors for Common Fixed Points in Banach Spaces
Esref Turkmen
2011-12-01
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.
Block Iterative Methods for a Finite Family of Relatively Nonexpansive Mappings in Banach Spaces
Takahashi Wataru
2007-01-01
Full Text Available 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 spaces.
Schuster, Thomas; Hofmann, Bernd; Kaltenbacher, Barbara
2012-10-01
Inverse problems can usually be modelled as operator equations in infinite-dimensional spaces with a forward operator acting between Hilbert or Banach spaces—a 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 term—theory 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 δ-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
Khinchin inequality and Banach-Saks type properties in rearrangement-invariant spaces
Sukochev, F
2010-01-01
{\\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.
Banach Gabor frames with Hermite functions: polyanalytic spaces from the Heisenberg group
Abreu, Luis Daniel; Grchenig, Karlheinz
2010-01-01
Gabor frames with Hermite functions are equivalent to sampling sequences in true Fock spaces of polyanalytic functions. In the L^2-case, such an equivalence follows from the unitarity of the polyanalytic Bargmann transform. We will introduce Banach spaces of polyanalytic functions and investigate the mapping properties of the polyanalytic Bargmann transform on modulation spaces. By applying the theory of coorbit spaces and localized frames to the Fock representation of the Heisenberg group, w...
Psi-exponential dichotomy for linear differential equations in a Banach space
Atanaska Georgieva
2013-07-01
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.
Nonuniform Exponential Stability and Instability of Evolution Operators in Banach Space
Mihaela Tomescu; Andrea Minda
2006-01-01
In this paper is presenting a parallel between nonuniform exponential stability and nonuniform exponential instability of evolution operators in Banach spaces, beginning to present the concept of the evolution operator with nonuniform exponential decay, respectively growth, next with the concept of the nonuniform stability, respectively instability, nonuniform exponential stability, respectively instability, nonuniform integrable stability, respectively instability and...
Nonuniform Exponential Stability and Instability of Evolution Operators in Banach Space
Mihaela Tomescu
2006-10-01
Full Text Available In this paper is presenting a parallel between nonuniform exponential stability and nonuniform exponential instability of evolution operators in Banach spaces, beginning to present the concept of the evolution operator with nonuniform exponential decay, respectively growth, next with the concept of the nonuniform stability, respectively instability, nonuniform exponential stability, respectively instability, nonuniform integrable stability, respectively instability and relationship between this concepts.
N-th order impulsive integro-differential equations in Banach spaces
Manfeng Hu
2004-03-01
Full Text Available We investigate the maximal and minimal solutions of initial value problem for N-th order nonlinear impulsive integro-differential equation in Banach space by establishing a comparison result and using the upper and lower solutions methods.
Known results and open problems on C1 linearization in Banach spaces
Munhoz Rodrigues, Hildebrando; Solà-Morales Rubió, Joan
2012-01-01
The purpose of this paper is to review the results obtained by the authors on linearization of dynamical systems in infinite dimen- sional Banach spaces, especially in the C 1 case, and also to present some open problems that we believe that are still important for the understanding of the theory.
Bound and periodic solutions of the Riccati equation in Banach space
A. Ya. Dorogovtsev
1995-01-01
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.
The generalized hardy operator with kernel and variable integral limits in banach function spaces
Lang J.; Gogatishvill A
1999-01-01
Let we have an integral operator where and are nondecreasing functions, and are non-negative and finite functions, and is nondecreasing in , nonincreasing in and for and . We show that the integral operator where and are Banach functions spaces with -condition is bounded if and only if . Where and
Convergence rates for an iteratively regularized Newton–Landweber iteration in Banach space
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)
On the fixed points of nonexpansive mappings in direct sums of Banach spaces
Wi?nicki, Andrzej
2011-01-01
We show that if a Banach space X has the weak fixed point property for nonexpansive mappings and Y has the generalized Gossez-Lami Dozo property or is uniformly convex in every direction, then the direct sum of X and Y with a strictly monotone norm has the weak fixed point property. The result is new even if Y is finite-dimensional.
Yuping Cao; Chuanzhi Bai
2014-01-01
We investigate boundary value problems for a coupled system of nonlinear fractional differential equations involving Caputo derivative in Banach spaces. A generalized singular type coupled Gronwall inequality system is given to obtain an important a priori bound. Existence results are obtained by using fixed point theorems and an example is given to illustrate the results.
On common fixed points of compatible mappings in metric and Banach spaces
M. S. Khan
1988-06-01
Full Text Available We prove a number of results concerning the existence of common fixed points of a family of maps satisfying certain contractive conditions in metric and Banach spaces. Results dealing with the stucture of the set of common fixed points of such maps are also given. Our work is an improvement upon the previously known results.
An existence theorem for a new class of multi-valued variational inclusion problems is established in smooth Banach spaces. Further, it is shown that a sequence of a Mann-type iteration algorithm is strongly convergent to the solutions in this class of variational inclusion problems. (author)
Integral equations of fractional order with multiple time delays in Banach spaces
Mouffak Benchohra
2012-04-01
Full Text Available In this article, we give sufficient conditions for the existence of solutions for an integral equation of fractional order with multiple time delays in Banach spaces. Our main tool is a fixed point theorem of Monch type associated with measures of noncompactness. Our results are illustrated by an example.
Approximate Fixed Point Theorems in Banach Spaces with Applications in Game Theory
2002-01-01
In this paper some new approximate fixed point theorems for multifunctions in Banach spaces are presented and a method is developed indicating how to use approximate fixed point theorems in proving the existence of approximate Nash equilibria for non-cooperative games.
Approximation Methods for Common Fixed Points of Mean Nonexpansive Mapping in Banach Spaces
Zhaohui Gu
2008-02-01
Full Text Available Let X be a uniformly convex Banach space, and let S,Â T be a pair of mean nonexpansive mappings. In this paper, it is proved that the sequence of Ishikawa iterations associated with S and T converges to the common fixed point of S and T.
Approximating common fixed points of two asymptotically quasi-nonexpansive mappings in Banach spaces
Isa Yildirim
2011-03-01
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.
Convergence to Compact Sets of Inexact Orbits of Nonexpansive Mappings in Banach and Metric Spaces
2009-02-01
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.
Gu Feng
2006-01-01
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.
A Bourgain-like property of Banach spaces with no copies of $c_0$
Pérez, A.; Raja, M
2016-01-01
We give a characterization of the existence of copies of $c_{0}$ in Banach spaces in terms of indexes. As an application, we deduce new proofs of James Distortion theorem and Bessaga-Pe{\\l}czynski theorem about weakly unconditionally Cauchy series.
Asymptotic behaviour of the solutions of Schroedinger equation with impulse effect in a Banach space
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
Wide and tight spherical hulls of bounded sets in Banach spaces
He, Chan; Wu, Senlin; Zhang, Xinling
2016-01-01
Let $A$ be a bounded closed convex set in a Banach space. The boundaries of the wide spherical hull $\\eta (A)$ and the tight spherical hull $\\theta (A)$ are characterized, the existence of diametral points of these three sets are discussed, and a further relation between these three sets is clarified. Moreover, a new characterization of balls is presented.
Xue-song Li
2009-01-01
Full Text Available We study the strong convergence of two kinds of viscosity iteration processes for approximating common fixed points of the pseudocontractive semigroup in uniformly convex Banach spaces with uniformly Gteaux differential norms. As special cases, we get the strong convergence of the implicit viscosity iteration process for approximating common fixed points of the nonexpansive semigroup in Banach spaces satisfying some conditions. The results presented in this paper extend and generalize some results concerned with the nonexpansive semigroup in (Chen and He, 2007 and the pseudocontractive mapping in (Zegeye et al., 2007 to the pseudocontractive semigroup in Banach spaces under different conditions.
Functional analysis an introduction to metric spaces, Hilbert spaces, and Banach algebras
Muscat, Joseph
2014-01-01
This textbook is an introduction to functional analysis suited to final year undergraduates or beginning graduates. Its various applications of Hilbert spaces, including least squares approximation, inverse problems, and Tikhonov regularization, should appeal not only to mathematicians interested in applications, but also to researchers in related fields. Functional Analysis adopts a self-contained approach to Banach spaces and operator theory that covers the main topics, based upon the classical sequence and function spaces and their operators. It assumes only a minimum of knowledge in elementary linear algebra and real analysis; the latter is redone in the light of metric spaces. It contains more than a thousand worked examples and exercises, which make up the main body of the book.
N. L. Braha
2005-05-01
Full Text Available In this paper we will give a characterization of 1-absolutely summing operators using μ-approximate l_1 sequences. Exactly if (x_n _1^∞ is μ-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.
Linear embeddings of finite-dimensional subsets of Banach spaces into Euclidean spaces
This paper treats the embedding of finite-dimensional subsets of a Banach space B into finite-dimensional Euclidean spaces. When the Hausdorff dimension of X ? X is finite, dH(X ? X) k are injective on X. The proof motivates the definition of the 'dual thickness exponent', which is the key to proving that a prevalent set of such linear maps have Hlder continuous inverse when the box-counting dimension of X is finite and k > 2dB(X). A related argument shows that if the Assouad dimension of X ? X is finite and k > dA(X ? X), a prevalent set of such maps are bi-Lipschitz with logarithmic corrections. This provides a new result for compact homogeneous metric spaces via the Kuratowksi embedding of (X, d) into L?(X)
Kriengsak Wattanawitoon
2011-01-01
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.
Inexact Newton–Landweber iteration for solving nonlinear inverse problems in Banach spaces
By making use of duality mappings, we formulate an inexact Newton–Landweber 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)
Buried object detection by means of a Lp Banach-space inversion procedure
Estatico, Claudio; Fedeli, Alessandro; Pastorino, Matteo; Randazzo, Andrea
2015-01-01
Electromagnetic inspection techniques are becoming powerful tools for buried object detection and subsurface prospection in several applicative fields, such as civil engineering and archeology. However, the nonlinearity and ill-posedness of the underlying inverse problem make the development of efficient imaging techniques a very challenging task. In the present paper, an algorithm based on a regularizing approach in Lp Banach spaces is proposed for tackling such problems. The effectiveness of the approach is verified by means of numerical simulations in a noisy environment aimed at evaluating the reconstruction capabilities with respect to the choice of several model parameters. The reported results show that, for small targets, the use of Lp Banach spaces with 1 < p < 2 allows to obtain a better localization of different buried scatterers.
Maximal regular boundary value problems in Banach-valued weighted space
Veli B. Shakhmurov
2005-02-01
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.
Some s-numbers of an integral operator of Hardy type in Banach function spaces
Edmunds, D.; Gogatishvili, Amiran; Kopaliani, T.; Samashvili, N.
2016-01-01
Roč. 207, July (2016), s. 79-97. ISSN 0021-9045 R&D Projects: GA ČR GA13-14743S Institutional support: RVO:67985840 Keywords : Hardy type operators * Banach function space s * s-numbers * compact linear operators Subject RIV: BA - General Mathematics Impact factor: 0.951, year: 2014 http://www.sciencedirect.com/science/article/pii/S0021904516000265
Some s-numbers of an integral operator of Hardy type in Banach function spaces
Edmunds, D.; Gogatishvili, Amiran; Kopaliani, T.; Samashvili, N.
2016-01-01
Roč. 207, July (2016), s. 79-97. ISSN 0021-9045 R&D Projects: GA ČR GA13-14743S Institutional support: RVO:67985840 Keywords : Hardy type operators * Banach function spaces * s-numbers * compact linear operators Subject RIV: BA - General Mathematics Impact factor: 0.951, year: 2014 http://www. science direct.com/ science /article/pii/S0021904516000265
A reinterpretation of set differential equations as differential equations in a Banach space
Rasmussen, Martin; Rieger, Janosch; Webster, Kevin
2015-01-01
Set differential equations are usually formulated in terms of the Hukuhara differential, which implies heavy restrictions for the nature of a solution. We propose to reformulate set differential equations as ordinary differential equations in a Banach space by identifying the convex and compact subsets of $\\R^d$ with their support functions. Using this representation, we demonstrate how existence and uniqueness results can be applied to set differential equations. We provide a simple example,...
Approximating Common Fixed Points of Lipschitzian Semigroup in Smooth Banach Spaces
Saeidi Shahram
2008-01-01
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 stron...
Tomonari Suzuki
2006-01-01
We prove Browder's type strong convergence theorems for infinite families of nonexpansive mappings. One of our main results is the following: let be a bounded closed convex subset of a uniformly smooth Banach space . Let be an infinite family of commuting nonexpansive mappings on . Let and be sequences in satisfying for . Fix and define a sequence in by for . Then converges strongly to , where is the unique sunny nonexpansive retraction from onto .
On the range of the derivative of Gâteaux-Smooth functions on separable Banach spaces
Deville, R.; Hájek, Petr Pavel
2005-01-01
Roč. 145, č. 2 (2005), s. 257-269. ISSN 0021-2172 R&D Projects: GA AV ČR(CZ) IAA1019003; GA AV ČR(CZ) IAA1019205; GA ČR(CZ) GA201/01/1198 Institutional research plan: CEZ:AV0Z10190503 Keywords : Gâteaux-Smooth functions * Banach space * Lipschitz function Subject RIV: BA - General Mathematics Impact factor: 0.448, year: 2005
Approximating fixed points of non-self asymptotically nonexpansive mappings in Banach spaces
Yongfu Su; Xiaolong Qin
2006-01-01
Suppose K is a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let T:K?E be an asymptotically nonexpansive mapping with {kn}?[1,?) such that ?n=1?(kn?1)
Some Results for a Finite Family of Uniformly L-Lipschitzian Mappings in Banach Spaces
Shih-Sen Chang; Jia Lin Huang; Xiong Rui Wang
2007-01-01
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).
Fixed point iteration for asymptotically quasi-nonexpansive mappings in Banach spaces
Somyot Plubtieng
2005-07-01
Full Text Available Suppose that C is a nonempty closed convex subset of a real uniformly convex Banach space X. Let T:CÃ¢Â†Â’C be an asymptotically quasi-nonexpansive mapping. In this paper, we introduce the three-step iterative scheme for such map with error members. Moreover, we prove that if T is uniformly L-Lipschitzian and completely continuous, then the iterative scheme converges strongly to some fixed point of T.
On some Banach space constants arising in nonlinear fixed point and eigenvalue theory
Erzakova Nina A
2004-01-01
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.
On some Banach space constants arising in nonlinear fixed point and eigenvalue theory
Martin Väth
2004-12-01
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.
Suzuki Tomonari
2006-01-01
Full Text Available We prove Browder's type strong convergence theorems for infinite families of nonexpansive mappings. One of our main results is the following: let be a bounded closed convex subset of a uniformly smooth Banach space . Let be an infinite family of commuting nonexpansive mappings on . Let and be sequences in satisfying for . Fix and define a sequence in by for . Then converges strongly to , where is the unique sunny nonexpansive retraction from onto .
Weak and Strong Convergence Theorems for Nonexpansive Mappings in Banach Spaces
Jing Zhao
2008-03-01
Full Text Available The purpose of this paper is to introduce two implicit iteration schemes for approximating fixed points of nonexpansive mapping T and a finite family of nonexpansive mappings {Ti}i=1N, respectively, in Banach spaces and to prove weak and strong convergence theorems. The results presented in this paper improve and extend the corresponding ones of H.-K. Xu and R. Ori, 2001, Z. Opial, 1967, and others.
Mann Type Implicit Iteration Approximation for Multivalued Mappings in Banach Spaces
Huimin He
2010-01-01
Full Text Available Let K be a nonempty compact convex subset of a uniformly convex Banach space E and let T be a multivalued nonexpansive mapping. For the implicit iterates x0?K, xn=?nxn-1+(1-?nyn, yn?Txn, n?1. We proved that {xn} converges strongly to a fixed point of T under some suitable conditions. Our results extended corresponding ones and revised a gap in the work of Panyanak (2007.
Hyers-Ulam stability of linear second-order differential equations in complex Banach spaces
Yongjin Li
2013-08-01
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.
Weak and Strong Convergence Theorems for Nonexpansive Mappings in Banach Spaces
Su Yongfu
2008-01-01
Full Text Available Abstract The purpose of this paper is to introduce two implicit iteration schemes for approximating fixed points of nonexpansive mapping and a finite family of nonexpansive mappings , respectively, in Banach spaces and to prove weak and strong convergence theorems. The results presented in this paper improve and extend the corresponding ones of H.-K. Xu and R. Ori, 2001, Z. Opial, 1967, and others.
Banach Gabor frames with Hermite functions: polyanalytic spaces from the Heisenberg group
Abreu, Luis Daniel
2010-01-01
Gabor frames with Hermite functions are equivalent to sampling sequences in true Fock spaces of polyanalytic functions. In the L^2-case, such an equivalence follows from the unitarity of the polyanalytic Bargmann transform. We will introduce Banach spaces of polyanalytic functions and investigate the mapping properties of the polyanalytic Bargmann transform on modulation spaces. By applying the theory of coorbit spaces and localized frames to the Fock representation of the Heisenberg group, we derive explicit polyanalytic sampling theorems which can be seen as a polyanalytic version of the lattice sampling theorem discussed by J. M. Whittaker in Chapter 5 of his book "Interpolatory Function Theory".
Embedding theorems in Banach-valued -spaces and maximal -regular differential-operator equations
Shakhmurov Veli B
2006-01-01
Full Text Available The embedding theorems in anisotropic Besov-Lions type spaces are studied; here and are two Banach spaces. The most regular spaces are found such that the mixed differential operators are bounded from to , where are interpolation spaces between and depending on and . By using these results the separability of anisotropic differential-operator equations with dependent coefficients in principal part and the maximal -regularity of parabolic Cauchy problem are obtained. In applications, the infinite systems of the quasielliptic partial differential equations and the parabolic Cauchy problems are studied.
On Linear Isometries of Banach Lattices in $\\mathcal{C}_0()$-Spaces
José M Isidro
2009-11-01
Consider the space $\\mathcal{C}_0()$ endowed with a Banach lattice-norm $\\|\\cdot p\\|$ that is not assumed to be the usual spectral norm $\\|\\cdot p\\|_∞$ of the supremum over . A recent extension of the classical Banach-Stone theorem establishes that each surjective linear isometry of the Banach lattice $(\\mathcal{C}_0(),\\|\\cdot p\\|)$ induces a partition of into a family of finite subsets $S\\subset$ along with a bijection $T:→$ which preserves cardinality, and a family $[u(S):S\\in]$ of surjective linear maps $u(S):\\mathcal{C}(T(S))→\\mathcal{C}(S)$ of the finite-dimensional *-algebras $\\mathcal{C}(S)$ such that $$(U f)|_{T(S)}=u(S)(f|_S) \\quad \\forall f\\in\\mathcal{C}_0() \\quad \\forall S\\in.$$ Here we endow the space of finite sets $S\\subset$ with a topology for which the bijection and the map are continuous, thus completing the analogy with the classical result.
Convergence on Composite Iterative Schemes for Nonexpansive Mappings in Banach Spaces
Jong Soo Jung
2008-05-01
Full Text Available Let E be a reflexive Banach space with a uniformly GÃƒÂ¢teaux 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:CÃ¢Â€Â‰Ã¢Â€Â‰Ã¢Â†Â’Ã¢Â€Â‰Ã¢Â€Â‰C a contractive mapping (or a weakly contractive mapping, and T:CÃ¢Â€Â‰Ã¢Â€Â‰Ã¢Â†Â’Ã¢Â€Â‰Ã¢Â€Â‰C nonexpansive mapping with the fixed point set F(TÃ¢Â€Â‰Ã¢Â€Â‰Ã¢Â‰Â Ã¢Â€Â‰Ã¢Â€Â‰Ã¢ÂˆÂ…. Let {xn} be generated by a new composite iterative scheme: yn=ÃŽÂ»nf(xn+(1Ã¢ÂˆÂ’ÃŽÂ»nTxn, xn+1=(1Ã¢ÂˆÂ’ÃŽÂ²nyn+ÃŽÂ²nTyn, (nÃ¢Â‰Â¥0. It is proved that {xn} converges strongly to a point in F(T, which is a solution of certain variational inequality provided that the sequence {ÃŽÂ»n}Ã¢ÂŠÂ‚(0,1 satisfies limnÃ¢Â†Â’Ã¢ÂˆÂžÃŽÂ»n=0 and Ã¢ÂˆÂ‘n=1Ã¢ÂˆÂžÃŽÂ»n=Ã¢ÂˆÂž, {ÃŽÂ²n}Ã¢ÂŠÂ‚[0,a for some 0
Casazza, Peter G.; Christensen, Ole
1995-01-01
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.
Convergence rates for the iteratively regularized Gauss–Newton method in Banach spaces
In this paper we consider the iteratively regularized Gauss–Newton 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. Hölder 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
Fixed Point Theorems for Suzuki Generalized Nonexpansive Multivalued Mappings in Banach Spaces
A. Abkar
2010-01-01
Full Text Available In the first part of this paper, we prove the existence of common fixed points for a commuting pair consisting of a single-valued and a multivalued mapping both satisfying the Suzuki condition in a uniformly convex Banach space. In this way, we generalize the result of Dhompongsa et al. (2006. In the second part of this paper, we prove a fixed point theorem for upper semicontinuous mappings satisfying the Suzuki condition in strictly L(? spaces; our result generalizes a recent result of Domnguez-Benavides et al. (2009.
Fixed Point Theorems for Suzuki Generalized Nonexpansive Multivalued Mappings in Banach Spaces
Abkar A
2010-01-01
Full Text Available In the first part of this paper, we prove the existence of common fixed points for a commuting pair consisting of a single-valued and a multivalued mapping both satisfying the Suzuki condition in a uniformly convex Banach space. In this way, we generalize the result of Dhompongsa et al. (2006. In the second part of this paper, we prove a fixed point theorem for upper semicontinuous mappings satisfying the Suzuki condition in strictly spaces; our result generalizes a recent result of Domnguez-Benavides et al. (2009.
On Borel structures in the Banach space C(\\beta\\omega)
Marciszewski, Witold; Plebanek, Grzegorz
2013-01-01
M. Talagrand showed that, for the Cech-Stone compactification \\beta\\omega\\ of the space of natural numbers, the norm and the weak topology generate different Borel structures in the Banach space C(\\beta\\omega). We prove that the Borel structures in C(\\beta\\omega) generated by the weak and the pointwise topology are also different. We also show that in C(\\omega*), where \\omega*=\\beta\\omega - \\omega, there is no countable family of pointwise Borel sets separating functions from C(\\omega*).
Variational Inequalities and Improved Convergence Rates for Tikhonov Regularisation on Banach Spaces
Grasmair, Markus
2011-01-01
In this paper we derive higher order convergence rates in terms of the Bregman distance for Tikhonov like convex regularisation for linear operator equations on Banach spaces. The approach is based on the idea of variational inequalities, which are, however, not imposed on the original Tikhonov functional, but rather on a dual functional. Because of that, the approach is not limited to convergence rates of lower order, but yields the same range of rates that is well known for quadratic regularisation on Hilbert spaces.
Evolutionary problems in non-reflexive spaces
Kružík, Martin; Zimmer, J.
2010-01-01
Roč. 16, č. 1 (2010), s. 1-22. ISSN 1262-3377 R&D Projects: GA AV ČR IAA1075402 Institutional research plan: CEZ:AV0Z10750506 Keywords : concentrations * energetic solution * energies with linear growth * oscillations * relaxation Subject RIV: BA - General Mathematics Impact factor: 1.084, year: 2009 http://library.utia.cas.cz/separaty/2008/MTR/kruzik-evolutionary problems in non-reflexive spaces.pdf
Bredies, Kristian
2009-01-01
We consider the task of computing an approximate minimizer of the sum of a smooth and a non-smooth convex functional, respectively, in Banach space. Motivated by the classical forward-backward splitting method for the subgradients in Hilbert space, we propose a generalization which involves the iterative solution of simpler subproblems. Descent and convergence properties of this new algorithm are studied. Furthermore, the results are applied to the minimization of Tikhonov-functionals associated with linear inverse problems and semi-norm penalization in Banach spaces. With the help of Bregman-Taylor-distance estimates, rates of convergence for the forward-backward splitting procedure are obtained. Examples which demonstrate the applicability are given, in particular, a generalization of the iterative soft-thresholding method by Daubechies, Defrise and De Mol to Banach spaces as well as total-variation-based image restoration in higher dimensions are presented.
Density of a semigroup in a Banach space
We study conditions on a set M in a Banach space X which are necessary or sufficient for the set R(M) of all sums x1+⋯+xn, xk∈M, to be dense in X. We distinguish conditions under which the closure R(M)-bar is an additive subgroup of X, and conditions under which this additive subgroup is dense in X. In particular, we prove that if M is a closed rectifiable curve in a uniformly convex and uniformly smooth Banach space X, and does not lie in a closed half-space {x∈X:f(x)≥0}, f∈X∗, and is minimal in the sense that every proper subarc of M lies in an open half-space {x∈X:f(x)>0}, then R(M)-bar =X. We apply our results to questions of approximation in various function spaces
Elke Wolf
2010-01-01
Full Text Available We consider analytic self-maps ø‑1,ø ‑2 of the open unit disk as well as analytic mapsψ 1, ψ2. These maps induce differences of weighted composition operators acting between weighted Banach spaces of holomorphic functions and weighted Bloch type spaces. In this article we give necessary and sufficient conditions for such a difference to be bounded resp. compact.Nosotros consideramos auto aplicaciones ø‑1,ø ‑2 del disco unitario abierto bien como aplicaciones analíticas ψ1, ψ2. Estas aplicaciones inducen diferencias de compición de operadores con peso actuando entre espacios de Banach pesados de funciones holomorfas y espacios de tipo Bloch con peso. En este artículo damos condiciones necesarias y suficientes para que tal diferencia sea acotada, respectivamente, compacta.
Some compactness tests in Banach spaces by Cesaro means of Fourier coefficients
Öztürk, Seda
2015-09-01
Let H be a complex Banach space, T be the topological group of the unit circle with respect to the Euclidean topology, α be a strongly continuous isometric linear representation of T in H, {Fkα}k ∈ℤ be the family of Fourier coefficients with respect to α, and {σkα}k ∈ℤ be Cesaro means of the family {Fkα}k ∈ℤ . In this work, we give some compactness tests for closed subsets of H.
Oscillation and the mean ergodic theorem for uniformly convex Banach spaces
Avigad, Jeremy; Rute, Jason
2012-01-01
Let B be a p-uniformly convex Banach space, with p >= 2. Let T be a linear operator on B, and let A_n x denote the ergodic average (1 / n) sum_{i< n} T^n x. We prove the following variational inequality in the case where T is power bounded from above and below: for any increasing sequence (t_k)_{k in N} of natural numbers we have sum_k || A_{t_{k+1}} x - A_{t_k} x ||^p
On the unbounded behaviour for some non-autonomous systems in Banach spaces
By modifying our previous methods and by using the notion of integral solution introduced by Benilan, we study the asymptotic behaviour of unbounded trajectories for the quasi-autonomous dissipative system: du/dt + Au is not an element of f where X is a real Banach space, A an accretive (possibly multivalued) operator in X x X, and f - f∞ is an element of Lp((0, +∞);X) for some f∞ is an element of X and 1 ≤ p < ∞. (author). 24 refs
C0-semigroups of linear operators on some ultrametric Banach spaces
Toka Diagana
2006-06-01
Full Text Available C0-semigroups of linear operators play a crucial role in the solvability of evolution equations in the classical context. This paper is concerned with a brief conceptualization of C0-semigroups on (ultrametric free Banach spaces E. In contrast with the classical setting, the parameter of a given C0-semigroup belongs to a clopen ball ÃŽÂ©r of the ground field K. As an illustration, we will discuss the solvability of some homogeneous p-adic differential equations.
Gabor multipliers for weighted Banach spaces on locally compact abelian groups
Pandey, S. S.
2009-01-01
We use a projective groups representation $\\rho$ of the unimodular group $\\mathcal{G} \\times \\hat{\\mathcal{G}}$ on $L^2(\\mathcal{G}$) to define Gabor wavelet transform of a function $f$ with respect to a window function $g$, where $\\mathcal{G}$ is a locally compact abelian group and $\\hat{\\mathcal{G}}$ its dual group. Using these transforms, we define a weighted Banach $\\mathcal{H}^{1, \\rho}_w(\\mathcal{G})$ and its antidual space $\\mathcal{H}^{{1}^{\\sim}, \\rho}_w(\\math...
On the regularity of mild solutions to complete higher order differential equations on Banach spaces
Nezam Iraniparast
2015-09-01
Full Text Available For the complete higher order differential equation u(n(t=Σk=0n-1Aku(k(t+f(t, t∈ R (* on a Banach space E, we give a new definition of mild solutions of (*. We then characterize the regular admissibility of a translation invariant subspace al M of BUC(R, E with respect to (* in terms of solvability of the operator equation Σj=0n-1AjXal Dj-Xal Dn = C. As application, almost periodicity of mild solutions of (* is proved.
Uniform-to-proper duality of geometric properties of Banach spaces and their ultrapowers
Talponen, Jarno
2014-01-01
In this note various geometric properties of a Banach space $X$ are characterized by means of weaker corresponding geometric properties involving an ultrapower $X^\\mathcal{U}$. The characterizations do not depend on the particular choice of the free ultrafilter $\\mathcal{U}$. For example, a point $x\\in S_X$ is an MLUR point if and only if $j(x)$ (given by the canonical inclusion $j\\colon X \\to X^\\mathcal{U}$) in $B_{X^\\mathcal{U}}$ is an extreme point; a point $x\\in S_X$ is LUR if and only if...
Approximating common fixed points of two asymptotically quasi-nonexpansive mappings in Banach spaces
Udomene Aniefiok
2006-01-01
Full Text Available Suppose is a nonempty closed convex subset of a real Banach space . Let be two asymptotically quasi-nonexpansive maps with sequences such that and , and . Suppose is generated iteratively by where and are real sequences in . It is proved that (a converges strongly to some if and only if ; (b if is uniformly convex and if either or is compact, then converges strongly to some . Furthermore, if is uniformly convex, either or is compact and is generated by , where , are bounded, are real sequences in such that and , are summable; it is established that the sequence (with error member terms converges strongly to some .
Toward a General Law of the Iterated Logarithm in Banach Space
Einmahl, Uwe
1993-01-01
A general bounded law of the iterated logarithm for Banach space valued random variables is established. Our results implies: (a) the bounded LIL of Ledoux and Talagrand, (b) a bounded LIL for random variables in the domain of attraction of a Gaussian law and (c) new LIL results for random variables outside the domain of attraction of a Gaussian law in cases where the classical norming sequence $\\{\\sqrt{nLLn}\\}$ does not work. Basic ingredients of our proof are an infinite-dimensional Fuk-Nag...
Maximal regular boundary value problems in Banach-valued function spaces and applications
Veli B. Shakhmurov
2006-07-01
Full Text Available The nonlocal boundary value problems for differential operator equations of second order with dependent coefficients are studied. The principal parts of the differential operators generated by these problems are non-selfadjoint. Several conditions for the maximal regularity and the Fredholmness in Banach-valued Lp-spaces of these problems are given. By using these results, the maximal regularity of parabolic nonlocal initial boundary value problems is shown. In applications, the nonlocal boundary value problems for quasi elliptic partial differential equations, nonlocal initial boundary value problems for parabolic equations, and their systems on cylindrical domain are studied.
Approximation of fixed points of Lipschitz pseudo-contractive mapping in Banach spaces
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
An analytic Koszul complex in a Banach space
Patyi, Imre
2005-01-01
We show that the holomorphic ideal sheaf of a linear section of a pseudoconvex open subset $\\Omega$ of, say, a Hilbert space $X=\\ell_2$ is acyclic. We also prove an analog of Hefer's lemma, i.e., if $f:\\Omega\\times\\Omega\\to\\CC$ is holomorphic and $f(x,x)=0$ for $x\\in\\Omega$, then there is a holomorphic $g:\\Omega\\times\\Omega\\to X^*$ with values in the dual space $X^*$ of $X$ such that $f(x,y)=g(x,y)(x-y)$
The Banach space $H^1(X,d,\\mu)$, II
Müller, Paul F. X.
1994-01-01
In this paper we give the isomorphic classification of atomic $H^1(X,d,\\mu)$, where $(X,d,\\mu)$ is a space of homogeneous type, hereby completing a line of investigation opened by the work of Bernard Maurey [Ma1], [Ma2], [Ma3] and continued by Lennard Carleson [C] and Przemyslaw Wojtaszczyk [Woj1], [Wpj2].
A characterization of subspaces of weakly compactly generated Banach spaces
Fabian, Marián; Montesinos, V.; Zizler, V.
2004-01-01
Roč. 69, č. 2 (2004), s. 457-464. ISSN 0024-6107 R&D Projects: GA ČR GA201/01/1198 Institutional research plan: CEZ:AV0Z1019905 Keywords : subspace of a weakly compactly generated space * Eberlein compact * epsilon-weakly compact set Subject RIV: BA - General Mathematics Impact factor: 0.663, year: 2004
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 results are considered in combination with finite-dimensional approximations for the space. An example is considered for illustration. (author). 15 refs
Ã¢Â„Â‚-convexity in infinite-dimensional Banach spaces and applications to Kergin interpolation
Lars Filipsson
2006-07-01
Full Text Available We investigate the concepts of linear convexity and Ã¢Â„Â‚-convexity in complex Banach spaces. The main result is that any Ã¢Â„Â‚-convex domain is necessarily linearly convex. This is a complex version of the Hahn-Banach theorem, since it means the following: given a Ã¢Â„Â‚-convex domain ÃŽÂ© in the Banach space X and a point pÃ¢ÂˆÂ‰ÃŽÂ©, there is a complex hyperplane through p that does not intersect ÃŽÂ©. We also prove that linearly convex domains are holomorphically convex, and that Kergin interpolation can be performed on holomorphic mappings defined in Ã¢Â„Â‚-convex domains.
A convergence rates result for an iteratively regularized Gauss–Newton–Halley method in Banach space
The use of second order information on the forward operator often comes at a very moderate additional computational price in the context of parameter identification problems for differential equation models. On the other hand the use of general (non-Hilbert) Banach spaces has recently found much interest due to its usefulness in many applications. This motivates us to extend the second order method from Kaltenbacher (2014 Numer. Math. at press), (see also Hettlich and Rundell 2000 SIAM J. Numer. Anal. 37 587620) to a Banach space setting and analyze its convergence. We here show rates results for a particular source condition and different exponents in the formulation of Tikhonov regularization in each step. This includes a complementary result on the (first order) iteratively regularized Gauss–Newton method in case of a one-homogeneous data misfit term, which corresponds to exact penalization. The results clearly show the possible advantages of using second order information, which get most pronounced in this exact penalization case. Numerical simulations for an inverse source problem for a nonlinear elliptic PDE illustrate the theoretical findings. (paper)
Rongfei Lin; Yueqing Zhao; Zdeněk Šmarda; Yasir Khan; Qingbiao Wu
2013-01-01
Newton-Kantorovich and Smale uniform type of convergence theorem of a deformed Newton method having the third-order convergence is established in a Banach space for solving nonlinear equations. The error estimate is determined to demonstrate the efficiency of our approach. The obtained results are illustrated with three examples.
Farrukh Mukhamedov
2010-01-01
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.
Arunchai Areerat
2011-01-01
Full Text Available Abstract In this article, we prove some results concerning the Krasnoselskii theorem on fixed points for the sum A + B of a weakly-strongly continuous mapping and an asymptotically nonexpansive mapping in Banach spaces. Our results encompass a number of previously known generalizations of the theorem.
Shin Min Kang
2008-08-01
Full Text Available In this paper we establish the strong convergence and almost stability of the Ishikawa iteration methods with errors for the iterative approximations of either fixed points of local strongly pseudocontractive operators or solutions of nonlinear operator equations with local strongly accretive type in real uniformly smooth Banach spaces. Our convergence results extend some known results in the literature.
Du, Fapeng; Chen, Jianlong
2016-01-01
In this paper, we characterize the perturbations of the Moore–Penrose metric generalized inverse of closed operator in Banach spaces. Under the condition $R(\\delta T)\\subset R(T)$ , $N(T)\\subset N(\\delta T)$ , respectively, we get some new results about upper-bound estimates of $\\|\\bar{T}^{M}\\|$ and $\\|\\bar{T}^{M}-T^{M}\\|$ .
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
Convergence of hybrid steepest descent method for variational inequalities in Banach spaces
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)
Models of CT dose profiles in Banach space; with applications to CT Dosimetry
Weir, Victor J
2015-01-01
This paper consists of two parts.In the first part, the scatter components of computed tomograpahy dose profiles are modeled using various functions including the solution to Riccati's differential equation. These scatter functions are combined with primary components such as a trapezoidal function and a constructed function that uses the analytic continuation of Heaviside step function. A mathematical theory is developed in Banach space. The modeled function, which is the product of the scatter and primary functions, is used to accurately fit data from the O-arm cone beam imaging system. In a second part of the paper, an approach to dosimtery is developed that shows that the results obtained from the use of a pencil shaped ion chamber is equivalent to that from a farmer chamber. This result is verified by presenting some preliminary experimental data measured in a 64 slice Siemens Sensation scanner.
Newton-Type Methods on Generalized Banach Spaces and Applications in Fractional Calculus
George A. Anastassiou
2015-10-01
Full Text Available We present a semilocal convergence study of Newton-type methods on a generalized Banach space setting to approximate a locally unique zero of an operator. Earlier studies require that the operator involved is Frchet differentiable. In the present study we assume that the operator is only continuous. This way we extend the applicability of Newton-type methods to include fractional calculus and problems from other areas. Moreover, under the same or weaker conditions, we obtain weaker sufficient convergence criteria, tighter error bounds on the distances involved and an at least as precise information on the location of the solution. Special cases are provided where the old convergence criteria cannot apply but the new criteria can apply to locate zeros of operators. Some applications include fractional calculus involving the Riemann-Liouville fractional integral and the Caputo fractional derivative. Fractional calculus is very important for its applications in many applied sciences.
Hybrid methods for accretive variational inequalities involving pseudocontractions in Banach spaces
Chen Rudong
2011-01-01
Full Text Available Abstract We use strongly pseudocontractions to regularize a class of accretive variational inequalities in Banach spaces, where the accretive operators are complements of pseudocontractions and the solutions are sought in the set of fixed points of another pseudocontraction. In this paper, we consider an implicit scheme that can be used to find a solution of a class of accretive variational inequalities. Our results improve and generalize some recent results of Yao et al. (Fixed Point Theory Appl, doi:10.1155/2011/180534, 2011 and Lu et al. (Nonlinear Anal, 71(3-4, 1032-1041, 2009. 2000 Mathematics subject classification 47H05; 47H09; 65J15
Hybrid Approximate Proximal Point Algorithms for Variational Inequalities in Banach Spaces
Yao JC
2009-01-01
Full Text Available Let be a nonempty closed convex subset of a Banach space with the dual , let be a continuous mapping, and let be a relatively nonexpansive mapping. In this paper, by employing the notion of generalized projection operator we study the variational inequality (for short, VI( : find such that for all , where is a given element. By combining the approximate proximal point scheme both with the modified Ishikawa iteration and with the modified Halpern iteration for relatively nonexpansive mappings, respectively, we propose two modified versions of the approximate proximal point scheme L. C. Ceng and J. C. Yao (2008 for finding approximate solutions of the VI( . Moreover, it is proven that these iterative algorithms converge strongly to the same solution of the VI( , which is also a fixed point of .
The split feasibility problem (SFP) consists of finding a common point in the intersection of finitely many convex sets, where some of the sets arise by imposing convex constraints in the range of linear operators. We are concerned with its solution in Banach spaces. To this end we generalize the CQ algorithm of Byrne with Bregman and metric projections to obtain an iterative solution method. In case the sets projected onto are contaminated with noise we show that a discrepancy principle renders this algorithm a regularization method. We measure the distance between convex sets by local versions of the Hausdorff distance, which in contrast to the standard Hausdorff distance allow us to measure the distance between unbounded sets. Hereby we prove a uniform continuity result for both kind of projections. The performance of the algorithm is demonstrated with some numerical experiments
The Solution by Iteration of a Composed K-Positive Definite Operator Equation in a Banach Space
Aneke, S. J.
2010-01-01
The equation = , where = + , with being a K-positive definite operator and being a linear operator, is solved in a Banach space. Our scheme provides a generalization to the so-called method of moments studied in a Hilbert space by Petryshyn (1962), as well as Lax and Milgram (1954). Furthermore, an application of the inverse function theorem provides simultaneously a general solution to this equation in some neighborhood of a point , where is Frchet differentiable and a...
Quasi-geostrophic equations with initial data in Banach spaces of local measures
Sadek Gala
2005-06-01
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.
Sokhuma, K.; A. Kaewkhao
2010-01-01
Let be a nonempty compact convex subset of a uniformly convex Banach space , and let and be a single-valued nonexpansive mapping and a multivalued nonexpansive mapping, respectively. Assume in addition that and for all . We prove that the sequence of the modified Ishikawa iteration method generated from an arbitrary by , , where and , are sequences of positive numbers satisfying , , converges strongly to a common fixed point of and ; that is, there exists such tha...
Vara Prasad KNVV
2006-01-01
Full Text Available Let be an arbitrary real Banach space and a nonempty, closed, convex (not necessarily bounded subset of . If is a member of the class of Lipschitz, strongly pseudocontractive maps with Lipschitz constant , then it is shown that to each Mann iteration there is a Krasnosleskij iteration which converges faster than the Mann iteration. It is also shown that the Mann iteration converges faster than the Ishikawa iteration to the fixed point of .
M. Eshaghi Gordji
2009-01-01
Full Text Available We establish the general solution of the functional equation f(nx+y+f(nx−y=n2f(x+y+n2f(x−y+2(f(nx−n2f(x−2(n2−1f(y for fixed integers n with n≠0,±1 and investigate the generalized Hyers-Ulam stability of this equation in quasi-Banach spaces.
Let E be a real uniformly convex Banach space whose dual space E* satisfies the Kadec- Klee property, K be a closed convex nonempty subset of E . Let T1, T2, . . . , Tm : K → K be asymptotically nonexpansive mappings of K into E with sequences (respectively) {kin}n=1∞ satisfying kin → 1 as n → ∞, i = 1, 2 , ...,m and Σn=1∞(kin - 1) in}n=1∞ be a sequence in [ε, 1 - ε ], for each i element of { 1, 2 , . . . ,m} (respectively). Let {xn} be a sequence generated for m ≥ 2 by, x1 element of K, xn+1 = (1 - α1n)xn + α1nT1nyn+m-2, yn+m-2 = (1 - α2n)xn + α2nT2nyn+m-3, ..., yn = (1 - αmn)xn + αmnTmnxn , n ≥ 1. Let Intersectioni=1m F (Ti) ≠ 0 . Then, {xn} converges weakly to a common fixed point of the family {Ti}i=1m. Under some appropriate condition on the family {Ti}i=1m, a strong convergence theorem is also roved. (author)
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
Approximating fixed points of non-self asymptotically nonexpansive mappings in Banach spaces
Yongfu Su
2006-01-01
Full Text Available Suppose K is a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let T:K?E be an asymptotically nonexpansive mapping with {kn}?[1,? such that ?n=1?(kn?10. Starting from arbitrary x1?K, define the sequence {xn} by x1?K, zn=P(?n''T(PTn?1xn+(1??n''xn, yn=P(?n'T(PTn?1zn+(1??n'xn, xn+1=P(?nT(PTn?1yn+(1??nxn. (i If the dual E* of E has the Kadec-Klee property, then { xn} converges weakly to a fixed point p?F(T; (ii if T satisfies condition (A, then {xn} converges strongly to a fixed point p?F(T.
Song, Guohui
2011-01-01
A typical approach in estimating the learning rate of a regularized learning scheme is to bound the approximation error by the sum of the sampling error, the hypothesis error and the regularization error. Using a reproducing kernel space that satisfies the linear representer theorem brings the advantage of discarding the hypothesis error from the sum automatically. Following this direction, we illustrate how reproducing kernel Banach spaces with the l1 norm can be applied to improve the learning rate estimate of l1-regularization in machine learning.
Dynamical Systems Method (DSM) for solving nonlinear operator equations in Banach spaces
Ramm, A G
2010-01-01
Let $F(u)=h$ be an operator equation in a Banach space $X$, $\\|F'(u)-F'(v)\\|\\leq \\omega(\\|u-v\\|)$, where $\\omega\\in C([0,\\infty))$, $\\omega(0)=0$, $\\omega(r)>0$ if $r>0$, $\\omega(r)$ is strictly growing on $[0,\\infty)$. Denote $A(u):=F'(u)$, where $F'(u)$ is the Fr\\'{e}chet derivative of $F$, and $A_a:=A+aI.$ Assume that (*) $\\|A^{-1}_a(u)\\|\\leq \\frac{c_1}{|a|^b}$, $|a|>0$, $b>0$, $a\\in L$. Here $a$ may be a complex number, and $L$ is a smooth path on the complex $a$-plane, joining the origin and some point on the complex $a-$plane, $00$ is a small fixed number, such that for any $a\\in L$ estimate (*) holds. It is proved that the DSM (Dynamical Systems Method) \\bee \\dot{u}(t)=-A^{-1}_{a(t)}(u(t))[F(u(t))+a(t)u(t)-f],\\quad u(0)=u_0,\\ \\dot{u}=\\frac{d u}{dt}, \\eee converges to $y$ as $t\\to +\\infty$, where $a(t)\\in L,$ $F(y)=f$, $r(t):=|a(t)|$, and $r(t)=c_4(t+c_2)^{-c_3}$, where $c_j>0$ are some suitably chosen constants, $j=2,3,4.$ Existence of a solution $y$ to the equation $F(u)=f$ is assumed. It is also assu...
Shkarin, Stanislav
2010-01-01
We construct an infinite dimensional non-unital Banach algebra $A$ and $a\\in A$ such that the sets $\\{za^n:z\\in\\C,\\ n\\in\\N\\}$ and $\\{({\\bf 1}+a)^na:n\\in\\N\\}$ are both dense in $A$, where $\\bf 1$ is the unity in the unitalization $A^{\\#}=A\\oplus \\spann\\{{\\bf 1}\\}$ of $A$. As a byproduct, we get a hypercyclic operator $T$ on a Banach space such that $T\\oplus T$ is non-cyclic and $\\sigma(T)=\\{1\\}$.
K. N. V. V. Vara Prasad
2007-01-01
Full Text Available Let E be an arbitrary real Banach space and K a nonempty, closed, convex (not necessarily bounded subset of E. If T is a member of the class of Lipschitz, strongly pseudocontractive maps with Lipschitz constant LÃ¢Â‰Â¥1, then it is shown that to each Mann iteration there is a Krasnosleskij iteration which converges faster than the Mann iteration. It is also shown that the Mann iteration converges faster than the Ishikawa iteration to the fixed point of T.
Hiroko Manaka
2010-01-01
Let E be a smooth Banach space with a norm $\\Vert \\cdot\\,\\!\\Vert $ . Let $V(x,y)={\\Vert x\\Vert}^{2}+{\\Vert y\\Vert }^{2}-2\\langle x,Jy\\rangle $ for any $x,y\\in E$ , where $\\langle \\cdot\\,\\!,\\cdot\\,\\!\\rangle $ stands for the duality pair and J is the normalized duality mapping. With respect to this bifunction $V(\\cdot\\,\\!,\\cdot\\,\\!)$ , a generalized nonexpansive mapping and a $V$ -strongly nonexpansive mapping are defined in $E$ . In this paper, using the properties of generalized nonexpansi...
Du, Fapeng; Xue, Yifeng
2012-01-01
In this paper, we investigate the invertibility of $I_Y+\\delta TT^+$ when $T$ is a closed operator from $X$ to $Y$ with a generalized inverse $T^+$ and $\\delta T$ is a linear operator whose domain contains $D(T)$ and range is contained in $D(T^+)$. The characterizations of the stable perturbation $T+\\delta T$ of $T$ by $\\delta T$ in Banach spaces are obtained. The results extend the recent main results of Huang's in Linear Algebra and its Applications.
On the Banach Problem on Surjections
Tokarev, Eugene
2002-01-01
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 essentially different f...
Metatext Phenomenon: Mode of Irony in Reflexive-Interpretative Space
Kuznetsova, Anna V.
2013-01-01
The article presents metatext and correlative interaction of irony in the reflexive-interpretative space of the literary text, clarifies the status of metatext space as linguo-cognitive activity of text producer. Irony serves as a system factor, forming metatext within the linguo-rhetoric script of text. Context plays special role in singling out of linguistic and discursive irony; multilevel character of irony is determined by context breadth, required for its decoding. The integrated nature...
Double-dual n-types over Banach spaces not containing Ã¢Â„Â“1
Markus Pomper
2004-07-01
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 EÃ¢Â€Â³ be the second dual of E and fix gÃ¢Â€Â³1,Ã¢Â€Â¦gÃ¢Â€Â³nÃ¢ÂˆÂˆEÃ¢Â€Â³. The function ÃÂ„:EÃƒÂ—Ã¢Â„ÂnÃ¢Â†Â’Ã¢Â„Â, defined by letting ÃÂ„(x,a1,Ã¢Â€Â¦,an=Ã¢Â€Â–x+Ã¢ÂˆÂ‘i=1naigÃ¢Â€Â³iÃ¢Â€Â– for all xÃ¢ÂˆÂˆE and all a1,Ã¢Â€Â¦,anÃ¢ÂˆÂˆÃ¢Â„Â, defines an n-type over E. Types that can be represented in this way are called double-dual n-types; we say that (gÃ¢Â€Â³1,Ã¢Â€Â¦gÃ¢Â€Â³nÃ¢ÂˆÂˆ(EÃ¢Â€Â³n realizes ÃÂ„. Let E be a (not necessarily separable Banach space that does not contain Ã¢Â„Â“1. We study the set of elements of (EÃ¢Â€Â³n 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 LÃƒÂ¶wenheim-Skolem theorem.
Ring homomorphisms on real Banach algebras
Sin-Ei Takahasi
2003-08-01
Full Text Available Let B be a strictly real commutative real Banach algebra with the carrier space ÃŽÂ¦B. If A is a commutative real Banach algebra, then we give a representation of a ring homomorphism ÃÂ:AÃ¢Â†Â’B, which needs not be linear nor continuous. If A is a commutative complex Banach algebra, then ÃÂ(A is contained in the radical of B.
Liang Yue
2011-01-01
Full Text Available Abstract The paper deals with the existence of positive solutions for Neumann boundary value problems of nonlinear second-order integro-differential equations - u ? ( t + M u ( t = f ( t , u ( t , ( S u ( t , 0 < t < 1 , u ? ( 0 = u ? ( 1 = ? and u ? ( t + M u ( t = f ( t , u ( t , ( S u ( t , 0 < t < 1 , u ? ( 0 = u ? ( 1 = ? in an ordered Banach space E with positive cone K, where M > 0 is a constant, f : [0, 1] K K ? K is continuous, S : C([0, 1], K ? C([0, 1], K is a Fredholm integral operator with positive kernel. Under more general order conditions and measure of noncompactness conditions on the nonlinear term f, criteria on existence of positive solutions are obtained. The argument is based on the fixed point index theory of condensing mapping in cones. Mathematics Subject Classification (2000: 34B15; 34G20.
Modification of Otolith Reflex Asymmetries Following Space Flight
Clarke, Andrew H.; Schoenfeld, Uwe; Wood, Scott J.
2011-01-01
We hypothesize that changes in otolith-mediated reflexes adapted for microgravity contribute to perceptual, gaze and postural disturbances upon return to Earth s gravity. Our goal was to determine pre- versus post-fight differences in unilateral otolith reflexes that reflect these adaptive changes. This study represents the first comprehensive examination of unilateral otolith function following space flight. Ten astronauts participated in unilateral otolith function tests three times pre-flight and up to four times after Shuttle flights from landing day through the subsequent 10 days. During unilateral centrifugation (UC, +/- 3.5cm at 400deg/s), utricular function was examined by the perceptual changes reflected by the subjective visual vertical (SVV) and by video-oculographic measurement of the otolith-mediated ocular counter-roll (OOR). Unilateral saccular reflexes were recorded by measurement of collic Vestibular Evoked Myogenic Potential (cVEMP). Although data from a few subjects were not obtained early post-flight, a general increase in asymmetry of otolith responses was observed on landing day relative to pre-flight baseline, with a subsequent reversal in asymmetry within 2-3 days. Recovery to baseline levels was achieved within 10 days. This fluctuation in the asymmetry measures appeared strongest for SVV, in a consistent direction for OOR, and in an opposite direction for cVEMP. These results are consistent with our hypothesis that space flight results in adaptive changes in central nervous system processing of otolith input. Adaptation to microgravity may reveal asymmetries in otolith function upon to return to Earth that were not detected prior to the flight due to compensatory mechanisms.
Some Extensions of Banach's Contraction Principle in Complete Cone Metric Spaces
Raja P
2008-01-01
Full Text Available Abstract In this paper we consider complete cone metric spaces. We generalize some definitions such as -nonexpansive and -uniformly locally contractive functions -closure, -isometric in cone metric spaces, and certain fixed point theorems will be proved in those spaces. Among other results, we prove some interesting applications for the fixed point theorems in cone metric spaces.
Some results on nearest points problems in Banach lattices
H. R. Khademzadeh
2015-04-01
Full Text Available In this paper we prove that for two equivalent norms such that $X$ becomes an STM and LLUM space the dominated best approximation problem have the same solution. We give some conditions such that under these conditions the Frchet differentiability of the nearest point map is equivalent to the continuity of metric projection in the dominated best approximation problem. Also we prove that these conditions are equivalent to strong solvability of the dominated best approximation problem. We prove these results in an STM, reflexive STM and UM spaces. In continuation we give some weaker conditions in the problem of best approximation. We delete the dominated condition and examine these results for a closed solid subset in Banach lattice. We prove that for two equivalent norms such that $X$ becomes an STM and LLUM space the best approximation problem have the same solution.
Networks for the weak topology of Banach and Fréchet spaces
Gabriyelyan, S.; Kąkol, Jerzy; Kubiś, Wieslaw; Marciszewski, W.
2015-01-01
Roč. 432, č. 2 (2015), s. 1183-1199. ISSN 0022-247X R&D Projects: GA ČR(CZ) GA14-07880S Institutional support: RVO:67985840 Keywords : Fréchet space * space of continuous functions * locally convex space Subject RIV: BA - General Mathematics Impact factor: 1.120, year: 2014 http://www.sciencedirect.com/science/article/pii/S0022247X15006836
Infinite-dimensional Grassmann-Banach algebras
Ivashchuk, V D
2000-01-01
A short review on infinite-dimensional Grassmann-Banach algebras (IDGBA) is presented. Starting with the simplest IDGBA over $K = {\\bf R}$ with $l_1$-norm (suggested by A. Rogers), we define a more general IDGBA over complete normed field $K$ with $l_1$-norm and set of generators of arbitrary power. Any $l_1$-type IDGBA may be obtained by action of Grassmann-Banach functor of projective type on certain $l_1$-space. In non-Archimedean case there exists another possibility for constructing of IDGBA using the Grassmann-Banach functor of injective type.
Reflexivity: The Creation of Liminal Spaces-Researchers, Participants, and Research Encounters.
Enosh, Guy; Ben-Ari, Adital
2016-03-01
Reflexivity is defined as the constant movement between being in the phenomenon and stepping outside of it. In this article, we specify three foci of reflexivity-the researcher, the participant, and the encounter-for exploring the interview process as a dialogic liminal space of mutual reflection between researcher and participant. Whereas researchers' reflexivity has been discussed extensively in the professional discourse, participants' reflexivity has not received adequate scholarly attention, nor has the promise inherent in reflective processes occurring within the encounter. PMID:25987582
Nonseparability of Banach spaces of bounded harmonic functions on Riemann surfaces
Nakai, Mitsuru
2011-01-01
The separability of certain seminormed spaces of harmonic functions on Riemann surfaces will be considered. An application of the result obtained in the above to some inverse inclusion problem in the classification theory of Riemann surfaces will be appended.
Group actions and ergodic theory on Banach function spaces / Richard John de Beer
De Beer, Richard John
2014-01-01
This thesis is an account of our study of two branches of dynamical systems theory, namely the mean and pointwise ergodic theory. In our work on mean ergodic theorems, we investigate the spectral theory of integrable actions of a locally compact abelian group on a locally convex vector space. We start with an analysis of various spectral subspaces induced by the action of the group. This is applied to analyse the spectral theory of operators on the space generated by measure...
Iterative approximation of the solution of a monotone operator equation in certain Banach spaces
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
Botelho, Fabio
2014-01-01
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.
Castro Gonzlez, Nieves; Vlez Cerrada, Jos Ygnacio
2008-01-01
En este trabajo se estudia la perturbacin de la inversa generalizada grupo en el mbito de los operadores lineales y acotados sobre un espacio de Banach complejo. Se 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 grupo y verifican ciertas condiciones geomtricas. Se...
Michał Podowski
1977-01-01
Full Text Available An operator equation of the following formλx = 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.
An operator equation of the following form lambda x = z + F(x), where z - an element of Banach space X and F(x) epsilonX for xepsilon DcX, is investigated. In the case 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 oscillations, are formulated. (author)
Infinite-dimensional Grassmann-Banach algebras
Ivashchuk, V. D.
2000-01-01
A short review on infinite-dimensional Grassmann-Banach algebras (IDGBA) is presented. Starting with the simplest IDGBA over $K = {\\bf R}$ with $l_1$-norm (suggested by A. Rogers), we define a more general IDGBA over complete normed field $K$ with $l_1$-norm and set of generators of arbitrary power. Any $l_1$-type IDGBA may be obtained by action of Grassmann-Banach functor of projective type on certain $l_1$-space. In non-Archimedean case there exists another possibility for constructing of I...
Escassut, Alain
2003-01-01
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
Qian Chen; Wei, W.; Xiang, X.(Department of Physics, Princeton University, Princeton, NJ, 08544, USA); JinRong Wang
2008-01-01
This paper studies the existence and global asymptotical stability of periodic PC-mild solution for the T-periodic Logistic system with time-varying generating operators and T0-periodic impulsive perturbations on Banach spaces. Two sufficient conditions that guarantee the exponential stability of the impulsive evolution operator corresponding to homogenous well-posed T-periodic system with time-varying generating operators and T0-periodic impulsive perturbations are given. It is shown that th...
Reduction of LieJordan Banach algebras and quantum states
In this paper, it is shown that the concept of dynamical correspondence for Jordan Banach algebras is equivalent to a Lie structure compatible with the Jordan one. Then a theory of reduction of LieJordan Banach algebras in the presence of quantum constraints is presented and compared to the standard reduction of C*-algebras of observables of a quantum system. The space of states of the reduced LieJordan Banach algebra is characterized in terms of Dirac states on the physical algebra of observables and its GNS representations described in terms of states on the unreduced algebra. (paper)
An inner product for a Banach-algebra
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
Spectral synthesis for Banach Algebras II
Feinstein, J. F.; Somerset, D. W. B.
1999-01-01
This paper continues the study of spectral synthesis and the topologies $\\tau_{\\infty}$ and $\\tau_r$ on the ideal space of a Banach algebra, concentrating particularly on the class of Haagerup tensor products of C$^*$-algebras. For this class, it is shown that spectral synthesis is equivalent to the Hausdorffness of $\\tau_{\\infty}$. Under a weak extra condition, spectral synthesis is shown to be equivalent to the Hausdorffness of $\\tau_r$.
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 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. The stability of the process in the stability of the vacuum state energy. 7 refs
Zhang Peiguo
2011-01-01
Full Text Available Abstract By obtaining intervals of the parameter λ, this article investigates the existence of a positive solution for a class of nonlinear boundary value problems of second-order differential equations with integral boundary conditions in abstract spaces. The arguments are based upon a specially constructed cone and the fixed point theory in cone for a strict set contraction operator. MSC: 34B15; 34B16.
Ferenczi, Valentin
1996-01-01
A Banach space $X$ is said to be Q.H.I. if eve\\-ry infinite dimensional quo\\-tient spa\\-ce of $X$ is H.I.: that is, a space is Q.H.I. if the H.I. property is not only stable passing to subspaces, but also passing to quotients and to the dual. We show that Gowers-Maurey's space is Q.H.I.; then we provide an example of a reflexive H.I. space ${\\cal X}$ whose dual is not H.I., from which it follows that $\\cal X$ is not Q.H.I.
Moduli and Characteristics of Monotonicity in Some Banach Lattices
Foralewski, P.; Hudzik, H.; Kaczmarek, R.; Krbec, Miroslav
-, - (2010), s. 852346. ISSN 1687-1812 R&D Projects: GA AV ČR IAA100190804; GA MŠk LC06052 Institutional research plan: CEZ:AV0Z10190503 Keywords : Banach lattice * characteristics of monotonicity * Orlicz function space * Orlicz sequence space Subject RIV: BA - General Mathematics http://www. fixed pointtheoryandapplications.com/content/2010/1/852346
Derivations into Duals of Ideals of Banach Algebras
M E Gorgi; T Yazdanpanah
2004-11-01
We introduce two notions of amenability for a Banach algebra $\\mathcal{A}$. Let be a closed two-sided ideal in $\\mathcal{A}$, we say $\\mathcal{A}$ is -weakly amenable if the first cohomology group of $\\mathcal{A}$ with coefficients in the dual space * is zero; i.e., $H^1(\\mathcal{A},I^*) =\\{0\\}$, and, $\\mathcal{A}$ is ideally amenable if $\\mathcal{A}$ is -weakly amenable for every closed two-sided ideal in $\\mathcal{A}$. We relate these concepts to weak amenability of Banach algebras. We also show that ideal amenability is different from amenability and weak amenability. We study the -weak amenability of a Banach algebra $\\mathcal{A}$ for some special closed two-sided ideal .
Additive Functional Inequalities in Banach Modules
An JongSu
2008-01-01
Full Text Available Abstract We investigate the following functional inequality in Banach modules over a -algebra and prove the generalized Hyers-Ulam stability of linear mappings in Banach modules over a -algebra in the spirit of the Th. M. Rassias stability approach. Moreover, these results are applied to investigate homomorphisms in complex Banach algebras and prove the generalized Hyers-Ulam stability of homomorphisms in complex Banach algebras.
Wave-front sets of Banach function types
Coriasco, Sandro; Toft, Joachim
2009-01-01
We introduce the wave-front set for distributions with respect to Fourier images of weighted translation invariant Banach function spaces. We prove that usual mapping properties for pseudo-differential operators hold in the context of such wave-front sets.
Endomorphic Elements in Banach Algebras
Babalola, V A
2004-01-01
The use of the properties of actions on an algebra to enrich the study of the algebra is well-trodden and still fashionable. Here, the notion and study of endomorphic elements of (Banach) algebras are introduced. This study is initiated, in the hope that it will open up, further, the structure of (Banach) algebras in general, enrich the study of endomorphisms and provide examples. In particular, here, we use it to classify algebras for the convenience of our study. We also present results on the structure of some classes of endomorphic elements and bring out the contrast with idempotents.
Zegeye, Habtu; Shahzad, Naseer
2014-01-01
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
Wagon, Stan
1985-01-01
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
Tensor products of abstract Besov spaces
Dmytryshyn M.I.
2012-01-01
We prove the interpolation theorem for tensor products of abstract Besov spaces, associated with closed operators in Banach spaces and show its application to the problems of approximations of elements of tensor products of Banach spaces.
Tensor products of abstract Besov spaces
Dmytryshyn M.I.
2012-12-01
Full Text Available We prove the interpolation theorem for tensor products of abstract Besov spaces, associated with closed operators in Banach spaces and show its application to the problems of approximations of elements of tensor products of Banach spaces.
Reflexive Aero Structures for Enhanced Survivability Project
National Aeronautics and Space Administration — Cornerstone Research Group Inc. (CRG) proposes to develop an advanced reflexive structure system to increase the survivability of aerostructures. This reflexive...
Several complex variables and Banach algebras
This paper aims to present certain applications of the theory of holomorphic functions of several complex variables to the study of commutative Banach algebras. The material falls into the following sections: (A) Introcution to Banach algebras (this will not presuppose any knowledge of the subject); (B) Groups of differential forms (mainly concerned with setting up a useful language); (C) Polynomially convex domains. (D) Holomorphic functional calculus for Banach algebras; (E) Some applications of the functional calculus. (author)
Projectivity of Banach and $C^*$-algebras of continuous fields
Cushing, David
2011-01-01
We give necessary and sufficient conditions for the left projectivity and biprojectivity of Banach algebras defined by locally trivial continuous fields of Banach algebras. We identify projective $C^*$-algebras $\\A$ defined by locally trivial continuous fields $\\mathcal{U} = \\{\\Omega,(A_t)_{t \\in \\Omega},\\Theta\\}$ such that each $C^*$-algebra $ A_{t}$ has a strictly positive element. For a commutative $C^*$-algebra $\\D$ contained in ${\\cal B}(H)$, where $H$ is a separable Hilbert space, we show that the condition of left projectivity of $\\D$ is equivalent to the existence of a strictly positive element in $\\D$ and so to the spectrum of $\\D$ being a Lindel$\\ddot{\\rm o}$f space.
Erratum to: “Polynomial algebras on classical Banach spaces”
D'Alessandro, Stefania; Hájek, Petr Pavel; Johanis, M.
2015-01-01
Roč. 207, č. 2 (2015), s. 1003-1012. ISSN 0021-2172 R&D Projects: GA ČR(CZ) GAP201/11/0345; GA MŠk(CZ) 7AMB12FR003 Institutional support: RVO:67985840 Keywords : Banach space * polynomial algebra Subject RIV: BA - General Mathematics Impact factor: 0.787, year: 2014 http://link.springer.com/article/10.1007%2Fs11856-015-1155-y
Bird, Alistair; Laustsen, Niels Jakob
2011-01-01
A theorem of Giesy and James states that $c_0$ is finitely representable in James' quasi-reflexive Banach space $J_2$. We extend this theorem to the $p$th quasi-reflexive James space $J_p$ for each $p \\in (1,\\infty)$. As an application, we obtain a new closed ideal of operators on $J_p$, namely the closure of the set of operators that factor through the complemented subspace $(\\ell_\\infty^1 \\oplus \\ell_\\infty^2 \\oplus...\\oplus \\ell_\\infty^n \\oplus...)_{\\ell_p}$ of $J_p$.
Rotund renormings in spaces of bochner integrable functions
Fabian, M.
2015-01-01
We show that if μ is a probability measure and X is a Banach space, then the Lebesgue-Bochner space L1(μ,X) admits an equivalent norm which is rotund (uniformly rotund in every direction, locally uniformly rotund, or midpoint locally uniformly rotund) if X does. We also prove that if X admits a uniformly rotund norm, then the space L1(μ,X) has an equivalent norm whose restriction to every reflexive subspace is uniformly rotund. This is done via the Luxemburg norm associated to a suitable Orli...
The normed and Banach envelopes of Weak L^1
Leung, Denny H.
1998-01-01
The space Weak L^1 consists of all measurable functions on [0,1] such that q(f) = sup_{c>0} c \\lambda{t : |f(t)| > c} is finite, where \\lambda denotes Lebesgue measure. Let \\rho be the gauge functional of the unit ball {f : q(f) \\leq 1} of the quasi- norm q, and let N be the null space of \\rho. The normed envelope of Weak L^1, which we denote by W, is the space (Weak L^1/N, \\rho). The Banach envelope of Weak L^1, \\overline{W}, is the completion of W. We show that \\overline{W} is isometrically...
Peterka, Robert J.
1993-01-01
Recent studies have identified significant correlations between space motion sickness susceptibility and measures of disconjugate torsional eye movements recorded during parabolic flights. These results support an earlier proposal which hypothesized that an asymmetry of otolith function between the two ears is the cause of space motion sickness. It may be possible to devise experiments that can be performed in the 1 g environment on earth that could identify and quantify the presence of asymmetric otolith function. This paper summarizes the known physiological and anatomical properties of the otolith organs and the properties of the torsional vestibulo-ocular reflex which are relevant to the design of a stimulus to identify otolith asymmetries. A specific stimulus which takes advantage of these properties is proposed.
Wood, Scott J.; Clarke, A. H.; Rupert, A. H.; Harm, D. L.; Clement, G. R.
2009-01-01
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.
BanachMazur Distance Between Convex Quadrangles
Lassak Marek
2014-12-01
Full Text Available It is proved that the Banach-Mazur distance between arbitrary two convex quadrangles is at most 2. The distance equals 2 if and only if the pair of these quadrangles is a parallelogram and a triangle.
Bounded Hochschild cohomology of Banach algebras with a matrix-like structure
Gronbaek, N
2003-01-01
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.
The Banach-Mazur-Schmidt game and the Banach-Mazur-McMullen game
Fishman, Lior; Reams, Vanessa; Simmons, David
2015-01-01
We introduce two new mathematical games, the Banach-Mazur-Schmidt game and the Banach-Mazur-McMullen game, merging well-known games. We investigate the properties of the games, as well as providing an application to Diophantine approximation theory, analyzing the geometric structure of certain Diophantine sets.
On the Cauchy Functional Inequality in Banach Modules
Park Choonkil
2008-01-01
Full Text Available Abstract We investigate the following functional inequality: in Banach modules over a -algebra, and prove the generalized Hyers-Ulam stability of linear mappings in Banach modules over a -algebra.
Banach-Mazur Games with Simple Winning Strategies
Grädel, Erich; Leßenich, Simon
2012-01-01
We discuss several notions of "simple" winning strategies for Banach-Mazur games on graphs, such as positional strategies, move-counting or length-counting strategies, and strategies with a memory based on finite appearance records (FAR). We investigate classes of Banach-Mazur games that are determined via these kinds of winning strategies. Banach-Mazur games admit stronger determinacy results than classical graph games. For instance, all Banach-Mazur games with omega-r...
Moduli and Characteristics of Monotonicity in Some Banach Lattices
Miroslav Krbec
2010-01-01
Full Text Available First the characteristic of monotonicity of any Banach lattice X is expressed in terms of the left limit of the modulus of monotonicity of X at the point 1. It is also shown that for Kthe spaces the classical characteristic of monotonicity is the same as the characteristic of monotonicity corresponding to another modulus of monotonicity ?^m,E. The characteristic of monotonicity of Orlicz function spaces and Orlicz sequence spaces equipped with the Luxemburg norm are calculated. In the first case the characteristic is expressed in terms of the generating Orlicz function only, but in the sequence case the formula is not so direct. Three examples show why in the sequence case so direct formula is rather impossible. Some other auxiliary and complemented results are also presented. By the results of Betiuk-Pilarska and Prus (2008 which establish that Banach lattices X with ?0,m(X<1 and weak orthogonality property have the weak fixed point property, our results are related to the fixed point theory (Kirk and Sims (2001.
Moduli and Characteristics of Monotonicity in Some Banach Lattices
Krbec Miroslav
2010-01-01
Full Text Available Abstract First the characteristic of monotonicity of any Banach lattice is expressed in terms of the left limit of the modulus of monotonicity of at the point . It is also shown that for Kthe spaces the classical characteristic of monotonicity is the same as the characteristic of monotonicity corresponding to another modulus of monotonicity . The characteristic of monotonicity of Orlicz function spaces and Orlicz sequence spaces equipped with the Luxemburg norm are calculated. In the first case the characteristic is expressed in terms of the generating Orlicz function only, but in the sequence case the formula is not so direct. Three examples show why in the sequence case so direct formula is rather impossible. Some other auxiliary and complemented results are also presented. By the results of Betiuk-Pilarska and Prus (2008 which establish that Banach lattices with and weak orthogonality property have the weak fixed point property, our results are related to the fixed point theory (Kirk and Sims (2001.
Connes-amenability of multiplier Banach algebras
Hayati, Bahman; Amini, Massoud
2010-01-01
Let $B$ be a Banach algebra with bounded approximate identity, and let $M(B)$ be its multiplier algebra. If there exists a continuous linear injection $B^{*}\\rightarrow M(B)$ such that, for every $b\\in B$ and every $u,v\\in B^{*}$ , $\\langle u,vb\\rangle_{B}=\\langle v,bu\\rangle_{B}$ , then $M(B)$ is a dual Banach algebra and the following are equivalent: ¶ (i) $B$ is amenable; ¶ (ii) $M(B)$ is Connes amenable; ¶ (iii) $M(B)$ has a normal, virtual diagonal.
Smooth renormings of the Lebesgue-Bochner function space L-1(mu, X)
Fabian, M.; Lajara, S.
2012-01-01
We show that, if μ is a probability measure and X is a Banach space, then the space L 1 (μ,X) of Bochner integrable functions admits an equivalent Gâteaux (or uniformly Gâteaux) smooth norm provided that X has such a norm, and that if X admits an equivalent Fréchet (resp. uniformly Fréchet) smooth norm, then L 1 (μ,X) has an equivalent renorming whose restriction to every reflexive subspace is Fréchet (resp. uniformly Fréchet) smooth.
On dominated polynomials between Banach spaces
Botelho, Geraldo; Rueda, Pilar
2008-01-01
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.
Spectral theory of linear operators and spectral systems in Banach algebras
Müller, Vladimir
2003-01-01
This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach algebras. It presents a survey of results concerning various types of spectra, both of single and n-tuples of elements. Typical examples are the one-sided spectra, the approximate point, essential, local and Taylor spectrum, and their variants. The theory is presented in a unified, axiomatic and elementary way. Many results appear here for the first time in a monograph. The material is self-contained. Only a basic knowledge of functional analysis, topology, and complex analysis is assumed. The monograph should appeal both to students who would like to learn about spectral theory and to experts in the field. It can also serve as a reference book. The present second edition contains a number of new results, in particular, concerning orbits and their relations to the invariant subspace problem. This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach alg...
Banach ultrapowers and multivalued nonexpansive mappings
Wisnicki, Andrzej; Wosko, Jacek
2007-02-01
The Banach ultrapower construction is applied in fixed point theory for multivalued mappings. We introduce the notion of ultra-asymptotic centers and use it to remove the separability assumption from the results of Dominguez Benavides, Lorenzo Ramirez (2004) and Dhompongsa, Kaewcharoen, Kaewkhao (2006).
Derivations And Cohomological Groups Of Banach Algebras
Azar, Kazem Haghnejad
2010-01-01
Let $B$ be a Banach $A-bimodule$ and let $n\\geq 0$. We investigate the relationships between some cohomological groups of $A$, that is, if the topological center of the left module action $\\pi_\\ell:A\\times B\\rightarrow B$ of $A^{(2n)}$ on $B^{(2n)}$ is $B^{(2n)}$ and $H^1(A^{(2n+2)},B^{(2n+2)})=0$, then we have $H^1(A,B^{(2n)})=0$, and we find the relationships between cohomological groups such as $H^1(A,B^{(n+2)})$ and $H^1(A,B^{(n)})$, spacial $H^1(A,B^*)$ and $H^1(A,B^{(2n+1)})$. We obtain some results in Connes-amenability of Banach algebras, and so for every compact group $G$, we conclude that $H^1_{w^*}(L^\\infty(G)^*,L^\\infty(G)^{**})=0$. Let $G$ be an amenable locally compact group. Then there is a Banach $L^1(G)-bimodule$ such as $(L^\\infty(G),.)$ such that $Z^1(L^1(G),L^\\infty(G))=\\{L_{f}:~f\\in L^\\infty(G)\\}.$ We also obtain some conclusions in the Arens regularity of module actions and weak amenability of Banach algebras. We introduce some new concepts as $left-weak^*-to-weak$ convergence property [...
Natural examples of Valdivia compact spaces
Kalenda, Ondrej F. K.
2008-04-01
We collect examples of Valdivia compact spaces, their continuous images and associated classes of Banach spaces which appear naturally in various branches of mathematics. We focus on topological constructions generating Valdivia compact spaces, linearly ordered compact spaces, compact groups, L1 spaces, Banach lattices and noncommutative L1 spaces.
(2-1)-Ideal amenability of triangular banach algebras
S Etemad; M Ettefagh
2015-05-01
Let $\\mathcal{A}$ and $\\mathcal{B}$ be two unital Banach algebras and let $\\mathcal{M}$ be an unital Banach $\\mathcal{A}$, $\\mathcal{B}$-module. Also, let $\\mathcal{T}=\\left[\\begin{smallmatrix} \\mathcal{A} & \\mathcal{M}\\\\ & \\mathcal{B}\\end{smallmatrix}\\right]$ be the corresponding triangular Banach algebra. Forrest and Marcoux (Trans. Amer. Math. Soc. 354 (2002) 1435–1452) have studied the -weak amenability of triangular Banach algebras. In this paper, we investigate (2-1)-ideal amenability of $\\mathcal{T}$ for all ≥ 1. We introduce the structure of ideals of these Banach algebras and then, we show that (2-1)-ideal amenability of $\\mathcal{T}$ depends on (2-1)-ideal amenability of Banach algebras $\\mathcal{A}$ and $\\mathcal{B}$.
Reflexive Aero Structures for Enhanced Survivability Project
National Aeronautics and Space Administration — Cornerstone Research Group Inc. (CRG) will develop an advanced reflexive structure technology system to increase the survivability of future systems constructed of...
Hereditary properties of Amenability modulo an ideal of Banach algebras
Hamidreza Rahimi
2014-10-01
Full Text Available In this paper we investigate some hereditary properties of amenability modulo an ideal of Banach algebras. We show thatif $(e_{\\alpha}_{\\alpha}$ is a bounded approximate identity modulo $I$ of a Banach algebra $A$ and $X$ is a neo-unital modulo $I$, then $(e_{\\alpha}_{\\alpha}$ is a bounded approximate identity for $X$. Moreover we show that amenability modulo an ideal of a Banach algebra $A$ can be only considered by the neo-unital modulo $I$ Banach algebra over $A$
Wood, S. J.; Clarke, A. H.; Rupert, A. H.; Harm, D. L.; Clement, G. R.
2009-01-01
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, centrifugation, and measure the time course of postflight 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.
On sequence spaces for Fr\\'echet frames
Pilipović, Stevan; Stoeva, Diana T.
2008-01-01
We analyze the construction of a sequence space $\\widetilde{\\Theta}$, resp. a sequence of sequence spaces, in order to have $\\{g_i\\}$ as a $\\widetilde{\\Theta}$-frame or Banach frame for a Banach space $X$, resp. pre-$F$-frame or $F$-frame for a Fr\\'echet space $X_F=\\cap_{s\\in {\\mathbb N}_0} X_s$, where $\\{X_s\\}_{s\\in {\\mathbb N}_0}$ is a sequence of Banach spaces.
Multipliers of Weighted Semigroups and Associated Beurling Banach Algebras
S J Bhatt; P A Dabhi; H V Dedania
2011-11-01
Given a weighted discrete abelian semigroup $(S,)$, the semigroup $M_(S)$ of -bounded multipliers as well as the Rees quotient $M_(S)/S$ together with their respective weights $\\overline{}$ and $\\overline{}_q$ induced by are studied; for a large class of weights , the quotient $\\ell^1(M_(S),\\overline{})/\\ell^1(S,)$ is realized as a Beurling algebra on the quotient semigroup $M_(S)/S$; the Gel’fand spaces of these algebras are determined; and Banach algebra properties like semisimplicity, uniqueness of uniform norm and regularity of associated Beurling algebras on these semigroups are investigated. The involutive analogues of these are also considered. The results are exhibited in the context of several examples.
A G.N.S.-type theorem for a non-involutive Banach algebra
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 (Hf, πf, ξf), where Hf is a Hilbert space with scalar product denoted by: , πf is a representation of A into L(Hf), the space of bounded linear operators on Hf, ξf is a cyclic vector in Hf, such that: f(x)=f(x)ξf, ξf >, 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, ω, ξ) 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
An inner product for a Banach-algebra
An intrinsic inner product for a commutative Banach*-algebra is defined. Several conditions for its completeness are established. It is shown that any Banach*-algebra with proper and continuous involution has an auxiliary norm that turns it into an A*-algebra. (author). 7 refs
Normas tensoriales construidas mediante espacios de sucesiones de Banach
Patricia Gmez Palacio
2003-01-01
Full Text Available En este art culo se de ne una norma tensorial gc a partir de un espacio de sucesiones de Banach . Para cada par de espacios de Banach E y F, se caracterizan los elementos de la complecci n del espacio E g F, Eb g F, y se caracteriza su espacio dual (E g F0
Compact multipliers on spaces of analytic functions
Mleczko, Paweł
2008-01-01
In the paper compact multiplier operators on Banach spaces of analytic functions on the unit disk with the range in Banach sequence lattices are studied. If the domain space $X$ is such that $H_\\infty\\hookrightarrow X\\hookrightarrow H_1$, necessary and sufficient conditions for compactness are presented. Moreover, the calculation of the Hausdorff measure of noncompactness for diagonal operators between Banach sequence lattices is applied to obtaining the characterization of compact multiplier...
Gordji, M E
2006-01-01
Let $X$ be a left introverted subspace of dual of a Banach algebra. We study $Z_t(X^*),$ the topological center of Banach algebra $X^*$. We fined the topological center of $(X\\cA)^*$, when $\\cA$ has a bounded right approximate identity and $\\cA\\subseteq X^*.$ So we introduce a new notation of amenability for a dual Banach algebra $\\cal A$. A dual Banach algebra $\\cal A$ is weakly Connes-amenable if the first $weak^*-$continuous cohomology group of $\\cal A$ with coefficients in $\\cal A$ is zero; i.e., $H^1_{w^*}(\\cal A, \\cal A)=\\{o\\}$. We study the weak Connes-amenability of some dual Banach algebras.
Wood, S. J.; Clarke, A. H.; Rupert, A. H.; Harm, D. L.; Clement, G. R.
2009-01-01
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, perception. A closed-loop nulling task is also performed with and without vibrotactile display feedback of chair radial position. PRELIMINARY RESULTS. 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. DISCUSSION. One result of this study will be to characterize the variability (gain, asymmetry) in both otolithocular responses and motion perception during variable radius centrifugation, and measure the time course of postflight 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.
Very Smooth Points of Spaces of Operators
T S S R K Rao
2003-02-01
In this paper we study very smooth points of Banach spaces with special emphasis on spaces of operators. We show that when the space of compact operators is an -ideal in the space of bounded operators, a very smooth operator attains its norm at a unique vector (up to a constant multiple) and ( ) is a very smooth point of the range space. We show that if for every equivalent norm on a Banach space, the dual unit ball has a very smooth point then the space has the Radon–Nikodým property. We give an example of a smooth Banach space without any very smooth points.
Veomett, Ellen
2010-01-01
Naor and Mendel's metric cotype extends the notion of the Rademacher cotype of a Banach space to all metric spaces. Every Banach space has metric cotype at least 2. We show that any metric space that is bi-Lipschitz equivalent to an ultrametric space has infinimal metric cotype 1. We discuss the invariance of metric cotype inequalities under snowflaking mappings and Gromov-Hausdorff limits, and use these facts to establish a partial converse of the main result.
Ideal Amenability of Banach Algebras on Locally Compact Groups
M Eshaghi Gordji; S A R Hosseiniun
2005-08-01
In this paper we study the ideal amenability of Banach algebras. Let $\\mathcal{A}$ be a Banach algebra and let be a closed two-sided ideal in $\\mathcal{A}, \\mathcal{A}$ is -weakly amenable if $H^1(\\mathcal{A},I^∗)=\\{0\\}$. Further, $\\mathcal{A}$ is ideally amenable if $\\mathcal{A}$ is -weakly amenable for every closed two-sided ideal in $\\mathcal{A}$. We know that a continuous homomorphic image of an amenable Banach algebra is again amenable. We show that for ideal amenability the homomorphism property for suitable direct summands is true similar to weak amenability and we apply this result for ideal amenability of Banach algebras on locally compact groups.
On Reflection: Is Reflexivity Necessarily Beneficial in Intercultural Education?
Blasco, Maribel
2012-01-01
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
General Hormander and Mikhlin conditions for multipliers of Besov spaces
Shahmurov, Rishad
2008-01-01
Here a new condition for the geometry of Banach spaces is introduced and the operator--valued Fourier multiplier theorems in weighted Besov spaces are obtained. Particularly, connections between the geometry of Banach spaces and Hormander-Mikhlin conditions are established. As an application of main results the regularity properties of degenerate elliptic differential operator equations are investigated.
Countable linear combinations of characters on commutative Banach algebras
Feinstein, J. F.
2014-01-01
An elegant but elementary result of Wolff from 1921, when interpreted in terms of Banach algebras, shows that it is possible to find a sequence of distinct characters $\\phi_n$ on the disc algebra and an $\\ell_1$ sequence of complex numbers $\\lambda_n$, not all zero, such that $\\sum_{n=1}^\\infty \\lambda_n \\phi_n =0.$ We observe that, even for general commutative, unital Banach algebras, this is not possible if the closure of the countable set of characters has no perfect subsets.
On the Cauchy Functional Inequality in Banach Modules
Choonkil Park
2008-05-01
Full Text Available We investigate the following functional inequality: Ã¢Â€Â–f(x+f(y+f(zÃ¢Â€Â–Ã¢Â‰Â¤Ã¢Â€Â–f(x+y+zÃ¢Â€Â– in Banach modules over a CÃ¢ÂˆÂ—-algebra, and prove the generalized Hyers-Ulam stability of linear mappings in Banach modules over a CÃ¢ÂˆÂ—-algebra.
Fell, James M G
1988-01-01
This is an all-encompassing and exhaustive exposition of the theory of infinite-dimensional Unitary Representations of Locally Compact Groups and its generalization to representations of Banach algebras. The presentation is detailed, accessible, and self-contained (except for some elementary knowledge in algebra, topology, and abstract measure theory). In the later chapters the reader is brought to the frontiers of present-day knowledge in the area of Mackey normal subgroup analysisand its generalization to the context of Banach *-Algebraic Bundles.
Almost Lie structures on an anchored Banach bundle
Cabau, Patrick
2011-01-01
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"
Emotionally Colorful Reflexive Games
Tarasenko, Sergey
2011-01-01
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.
Di Girolami, Cristina
2011-01-01
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)...
Reflexive intensification in Spanish: Toward a complex reflexive?
Pedersen, Johan
Spanish, intensifier, intensification, reflexive pronouns, anaphor, reanalysis, grammaticalization, sí, mismo......Spanish, intensifier, intensification, reflexive pronouns, anaphor, reanalysis, grammaticalization, sí, mismo...
Krogsgaard, Michael R; Dyhre-Poulsen, Poul; Fischer-Rasmussen, Torsten
2002-01-01
The idea of muscular reflexes elicited from sensory nerves of the cruciate ligaments is more than 100 years old, but the existence of such reflexes has not been proven until the recent two decades. First in animal experiments, a muscular excitation could be elicited in the hamstrings when the ant...
A generalization of the weak amenability of some Banach algebra
Azar, Kazem Haghnejad
2010-01-01
Let $A$ be a Banach algebra and $A^{**}$ be the second dual of it. We show that by some new conditions, $A$ is weakly amenable whenever $A^{**}$ is weakly amenable. We will study this problem under generalization, that is, if $(n+2)-th$ dual of $A$, $A^{(n+2)}$, is $T-S-$weakly amenable, then $A^{(n)}$ is $T-S-$weakly amenable where $T$ and $S$ are continuous linear mappings from $A^{(n)}$ into $A^{(n)}$.
The Socle and Finite Dimensionality of some Banach Algebras
Ali Ghaffari; Ali Reza Medghalchi
2005-08-01
The purpose of this note is to describe some algebraic conditions on a Banach algebra which force it to be finite dimensional. One of the main results in Theorem 2 which states that for a locally compact group , is compact if there exists a measure in $\\mathrm{Soc} (L^1(G))$ such that () ≠ 0. We also prove that is finite if $\\mathrm{Soc}(M(G))$ is closed and every nonzero left ideal in () contains a minimal left ideal.
Petrov, S.
2000-08-20
An information system is reflexive if it stores a description of its current structure in the body of stored information and is acting on the base of this information. A data model is reflexive, if its language is meta-closed and can be used to build such a system. The need for reflexive data models in new areas of information technology applications is argued. An attempt to express basic notions related to information systems is made in the case when the system supports and uses meta-closed representation of the data.
Convexity and w*-compactness in Banach spaces
Granero, A. S.; Hájek, Petr Pavel; Santalucía, V. M.
2004-01-01
Roč. 328, č. 4 (2004), s. 625-631. ISSN 0025-5831 R&D Projects: GA ČR GA201/01/1198; GA AV ČR IAA1019205 Institutional research plan: CEZ:AV0Z1019905 Keywords : krein theorem * weak compactness Subject RIV: BA - General Mathematics Impact factor: 0.790, year: 2004
Stability of stationary and periodic solutions equations in Banach space
A. Ya. Dorogovtsev
1997-01-01
Full Text Available Linear difference and differential equations with operator coefficients and random stationary (periodic input are considered. Conditions are presented for the mean stability of stationary (periodic solutions under small perturbation of the coefficients.
Stochastic processes on non-Archimedean Banach spaces
Ludkovsky, S. V.
2003-01-01
Non-Archimedean analogs of Markov quasimeasures and stochastic processes are investigated. They are used for the development of stochastic antiderivations. The non-Archimedean analog of the ItÃƒÂ´ formula is proved.
Smooth linearization for a saddle on Banach spaces
Munhoz Rodrigues, Hildebrando; Solà-Morales Rubió, Joan
2003-01-01
As a continuation of a previous work on linearization of class C1 of diﬀeomorphisms and ﬂows in inﬁnite dimensions near a ﬁxed point, in this work we deal with the case of a saddle point with some non-resonance restrictions for the linear part. Our result can be seen as an extension of results by P. Hartman [2] and Aronson, Belitskii and Zhuzhoma [1] in dimension two. We also present an application to a system of nonlinear wave equations.
Existence theorems for functional differential equations in Banach spaces
Sghir, A
2009-01-01
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].
Lectures given at the Banach Center and C.I.M.E. Joint Summer School
Lachowicz, Mirosław
2008-01-01
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.
Functional calculus extensions on dual spaces
Terauds, Venta
2008-01-01
In this note, we show that if a Banach space X has a predual, then every bounded linear operator on X with a continuous functional calculus admits a bounded Borel functional calculus. A consequence of this is that on such a Banach space, the classes of finitely spectral and prespectral operators coincide. We also apply this result to give some sufficient conditions for an operator with an absolutely continuous functional calculus to admit a bounded Borel one.
Identification of Spinal Reflexes:
Vlugt, E. de
2004-01-01
Visco-elasticity of joints is important for the maintenance of the human body posture and can in two manners be regulated. By means of cocontraction of antagonistic muscle groups and by neural reflexive feedback of muscle length and muscle strength, measured both by means of sensors in the muscles. The impact of the reflexive regulation is considerable and infestation of this system can give serious motor deviations, like at the Parkinson's Disease. Except anatomical knowledge is there still ...
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.
Orthogonalities, transitivity of norms and characterizations of Hilbert spaces
Martini, Horst; Wu, Senlin
2015-01-01
We introduce three concepts, called $I$-vector, $IP$-vector, and $P$-vector, which are related to isosceles orthogonality and Pythagorean orthogonality in normed linear spaces. Having the Banach-Mazur rotation problem in mind, we prove that an almost transitive real Banach space, whose dimension is at least three and which contains an $I$-vector (an $IP$-vector, a $P$-vector, or a unit vector whose pointwise James constant is $\\sqrt2$, respectively) is a Hilbert space.
Ratner, Helene
What Danish school managers can teach STS researchers about epistemological ideals and pragmatic morals. Reflexivity has an ambivalent status in both anthropology and Science and Technology Studies. On the one hand, the critique of representation at the heart of the reflexivity debates of the 1980s...... highlighted non-symmetric relationships between observer and observed and accused the academic text of enacting a realist genre, concealing the relativism entailed in textual production (Clifford and Marcus 1986, Woolgar 1988, Ashmore 1989). On the other hand, the reflexivity program produced fears of a...... “corrosive relativism in which everything is but a more or less clever expression of opinion” (Geertz 1988:2, 3) and it has suffered the little flattering accusations of piling "layer upon layer of self-consciousness to no avail" (Latour 1988:170) with little “interest [for] … theoretically ambitious...
Corneomandibular reflex: Anatomical basis
Michele Pistacchi
2015-01-01
Full Text Available Corneomandibular reflex is a pathological phenomenon evident in cases of severe brainstem damage. It is considered to be a pathological exteroceptive reflex, associated with precentro bulbar tract lesions. The sign is useful in distinguishing central neurological injuries to metabolic disorders in acutely comatose patients, localizing lesions to the upper brainstem area, determining the depth of coma and its evolution, providing evidence of uncal or transtentorial herniation in acute cerebral hemisphere lesions, and it is a marker of supraspinal level impairment in amyotrophic lateral sclerosis and multiple sclerosis. This sign was evident in a patient with severe brain damage. We discuss the literature findings and its relevance in prognosis establishment.
Geometry of Mntz spaces and related questions
Gurariy, Vladimir
2005-01-01
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.
Sharp form of the Sobolev trace theorems. [Proof of trace theorems for Besov spaces
Scott, R.
1977-05-01
Trace theorems for Besov spaces are proved by use of piecewise polynomial approximation theory and the K-method of interpolating Banach spaces. These theorems are limiting cases of standard embedding results.
Filtrations of Totally Reflexive Modules
Tracy, Denise A. Rangel
2014-01-01
In this paper, we will introduce a subcategory of totally reflexive modules that have a saturated filtration by other totally reflexive modules. We will prove these are precisely the totally reflexive modules with an upper-triangular presentation matrix. We conclude with an investigation of the ranks of $\\operatorname{Ext}^1$ of two such modules over a specific ring.
Sweeney, Mary M.; Urcuioli, Peter J.
2010-01-01
A recent theory of pigeons' equivalence-class formation (Urcuioli, 2008) predicts that reflexivity, an untrained ability to match a stimulus to itself, should be observed after training on two "mirror-image" symbolic successive matching tasks plus identity successive matching using some of the symbolic matching stimuli. One group of pigeons was…
Rassias JM
2009-01-01
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.
Characterizing Hilbert spaces using Fourier transform over the field of p-adic numbers
Radyna, Yauhen; Radyno, Yakov; Sidorik, Anna
2008-01-01
We characterize Hilbert spaces in the class of all Banach spaces using Fourier transform of vector-valued functions over the field $Q_p$ of $p$-adic numbers. Precisely, Banach space $X$ is isomorphic to a Hilbert one if and only if Fourier transform $F: L_2(Q_p,X)\\to L_2(Q_p,X)$ in space of functions, which are square-integrable in Bochner sense and take value in $X$, is a bounded operator.
Bapurao C. Dhage
2006-03-01
Full Text Available In this paper, we prove an existence theorem for hyperbolic differential equations in Banach algebras under Lipschitz and Caratheodory conditions. The existence of extremal solutions is also proved under certain monotonicity conditions.
Simplified and Equivalent Characterizations of Banach Limit Functional and Strong Almost Convergence
You, Chao
2009-01-01
In this paper, we give simplified and equivalent characterizations of Banach limit functional, which is the minimum requirement to characterize strong almost convergence. With this machinery, we show that Hajdukovic's quasi-almost convergence is equivalent to strong almost convergence.
Said Abbas
2010-07-01
Full Text Available This article studies the existence of solutions and extremal solutions to partial hyperbolic differential equations of fractional order with impulses in Banach algebras under Lipschitz and Caratheodory conditions and certain monotonicity conditions.
Mentalis muscle related reflexes.
Gündüz, Ayşegül; Uyanık, Özlem; Ertürk, Özdem; Sohtaoğlu, Melis; Kızıltan, Meral Erdemir
2016-05-01
The mentalis muscle (MM) arises from the incisive fossa of the mandible, raises and protrudes the lower lip. Here, we aim to characterize responses obtained from MM by supraorbital and median electrical as well as auditory stimuli in a group of 16 healthy volunteers who did not have clinical palmomental reflex. Reflex activities were recorded from the MM and orbicularis oculi (O.oc) after supraorbital and median electrical as well as auditory stimuli. Response rates over MM were consistent after each stimulus, however, mean latencies of MM response were longer than O.oc responses by all stimulation modalities. Shapes and amplitudes of responses from O.oc and MM were similar. Based on our findings, we may say that MM motoneurons have connections with trigeminal, vestibulocochlear and lemniscal pathways similar to other facial muscles and electrophysiological recording of MM responses after electrical and auditory stimulation is possible in healthy subjects. PMID:26721248
Reflex Sympathetic Dystrophy Syndrome
Annil Mahajan, Pawan Suri, Ghulam Hussain Bardi, J.B. Singh, Dheeraj Gandotra, Vijay Gupta
2004-01-01
Reflex Sympathetic Dystrophy (RSD) or Complex Regional Pain Syndome Type-I (CRPS-I), adisease of unknown prevalance, complicates any minor trauma, stroke, myocardial infection, colle’sfracture, peripheral nerve injury and in one-fourth of cases without any precipitant factor. Anawareness of RSD and the injuries, illnesses and drugs that can provoke it is the first step to learnfor an early treatment and better outcome. Here we present a neglected case of RSD followingminor trauma who presente...
Corporeal reflexivity and autism.
Ochs, Elinor
2015-06-01
Ethnographic video recordings of high functioning children with autism or Aspergers Syndrome in everyday social encounters evidence their first person perspectives. High quality visual and audio data allow detailed analysis of children's bodies and talk as loci of reflexivity. Corporeal reflexivity involves displays of awareness of one's body as an experiencing subject and a physical object accessible to the gaze of others. Gaze, demeanor, actions, and sotto voce commentaries on unfolding situations indicate a range of moment-by-moment reflexive responses to social situations. Autism is associated with neurologically based motor problems (e.g. delayed action-goal coordination, clumsiness) and highly repetitive movements to self-soothe. These behaviors can provoke derision among classmates at school. Focusing on a 9-year-old girl's encounters with peers on the playground, this study documents precisely how autistic children can become enmeshed as unwitting objects of stigma and how they reflect upon their social rejection as it transpires. Children with autism spectrum disorders in laboratory settings manifest diminished understandings of social emotions such as embarrassment, as part of a more general impairment in social perspective-taking. Video ethnography, however, takes us further, into discovering autistic children's subjective sense of vulnerability to the gaze of classmates. PMID:25939529
Composition operators on vector-valued analytic function spaces: a survey
Laitila, Jussi; Tylli, Hans-Olav
2015-01-01
We survey recent results about composition operators induced by analytic self-maps of the unit disk in the complex plane on various Banach spaces of analytic functions taking values in infinite-dimensional Banach spaces. We mostly concentrate on the research line into qualitative properties such as weak compactness, initiated by Liu, Saksman and Tylli (1998), and continued in several other papers. We discuss composition operators on strong, respectively weak, spaces of vector-valued analytic ...
Soleus stretch reflex during cycling
Grey, Michael James; Pierce, C. W.; Milner, T. E.; Sinkjær, Thomas
2001-01-01
The modulation and strength of the human soleus short latency stretch reflex was investigated by mechanically perturbing the ankle during an unconstrained pedaling task. Eight subjects pedaled at 60 rpm against a preload of 10 Nm. A torque pulse was applied to the crank at various positions durin...... depressed during active cycling as has been shown with the H-reflex. This lack of depression may reflect a decreased susceptibility of the stretch reflex to inhibition, possibly originating from presynaptic mechanisms....
Best approximation in Orlicz spaces
S. Ayesh
1991-06-01
Full Text Available Let X be a real Banach space and (ÃŽÂ©,ÃŽÂ¼ be a finite measure space and ÃÂ• be a strictly icreasing convex continuous function on [0,Ã¢ÂˆÂž with ÃÂ•(0=0. The space LÃÂ•(ÃŽÂ¼,X is the set of all measurable functions f with values in X such that Ã¢ÂˆÂ«ÃŽÂ©ÃÂ•(Ã¢Â€Â–cÃ¢ÂˆÂ’1f(tÃ¢Â€Â–dÃŽÂ¼(t0. One of the main results of this paper is: Ã‚Â“For a closed subspace Y of X, LÃÂ•(ÃŽÂ¼,Y is proximinal in LÃÂ•(ÃŽÂ¼,X if and only if L1(ÃŽÂ¼,Y is proximinal in L1(ÃŽÂ¼,XÃ¢Â€Â²Ã¢Â€Â‹Ã¢Â€Â². As a result if Y is reflexive subspace of X, then LÃÂ•(ÃÂ•,Y is proximinal in LÃÂ•(ÃŽÂ¼,X. Other results on proximinality of subspaces of LÃÂ•(ÃŽÂ¼,X are proved.
Reflex Sympathetic Dystrophy Syndrome
Annil Mahajan, Pawan Suri, Ghulam Hussain Bardi, J.B. Singh, Dheeraj Gandotra, Vijay Gupta
2004-07-01
Full Text Available Reflex Sympathetic Dystrophy (RSD or Complex Regional Pain Syndome Type-I (CRPS-I, adisease of unknown prevalance, complicates any minor trauma, stroke, myocardial infection, colle’sfracture, peripheral nerve injury and in one-fourth of cases without any precipitant factor. Anawareness of RSD and the injuries, illnesses and drugs that can provoke it is the first step to learnfor an early treatment and better outcome. Here we present a neglected case of RSD followingminor trauma who presented to us after 6-7 months of onset of disease. Delay in treatment resultedin partial recovery of the patient.
Approximately
Karimi T; Kaboli Gharetapeh S; Gordji MEshaghi
2009-01-01
Let , and let be two rings. An additive map is called -Jordan homomorphism if for all . In this paper, we establish the Hyers-Ulam-Rassias stability of -Jordan homomorphisms on Banach algebras. Also we show that (a) to each approximate 3-Jordan homomorphism from a Banach algebra into a semisimple commutative Banach algebra there corresponds a unique 3-ring homomorphism near to , (b) to each approximate -Jordan homomorphism between two commutative Banach algebras there corresp...
Acoustic reflex and general anaesthesia.
Farkas, Z
1983-01-01
Infant and small children are not always able to cooperate in impedance measurements. For this reason it was decided, -in special cases, -to perform acoustic reflex examination under general anaesthesia. The first report on stapedius reflex and general anaesthesia was published by Mink et al. in 1981. Under the effect of Tiobutabarbital, Propanidid and Diazepam there is no reflex response. Acoustic reflex can be elicited with Ketamin-hydrochlorid and Alphaxalone-alphadolone acetate narcosis. The reflex threshold remains unchanged and the amplitude of muscle contraction is somewhat increased. The method was used: 1. to assess the type and degree of hearing loss in children with cleft palate and/or lip prior to surgery. 2. to exclude neuromuscular disorders with indication of pharyngoplasties. 3. to quantify hearing level in children--mostly multiply handicapped--with retarded speech development. The results of Behavioral Observation and Impedance Audiometry are discussed and evaluated. PMID:6577558
[Reflex seizures, cinema and television].
Olivares-Romero, Jesús
2015-12-16
In movies and television series are few references to seizures or reflex epilepsy even though in real life are an important subgroup of total epileptic syndromes. It has performed a search on the topic, identified 25 films in which they appear reflex seizures. Most seizures observed are tonic-clonic and visual stimuli are the most numerous, corresponding all with flashing lights. The emotions are the main stimuli in higher level processes. In most cases it is not possible to know if a character suffers a reflex epilepsy or suffer reflex seizures in the context of another epileptic syndrome. The main conclusion is that, in the movies, the reflex seizures are merely a visual reinforcing and anecdotal element without significant influence on the plot. PMID:26662874
Mierczyński, Janusz; Shen, Wenxian
2012-01-01
This is the first of a series of papers concerned with principal Lyapunov exponents and principal Floquet subspaces of positive random dynamical systems in ordered Banach spaces. It focuses on the development of general theory. First, the notions of generalized principal Floquet subspaces, generalized principal Lyapunov exponents, and generalized exponential separations for general positive random dynamical systems in ordered Banach spaces are introduced, which extend the classical notions of...
Finiteness of the space of n-cycles for a n-concave complex space
2015-01-01
We show that for n $\\ge$ 2 the space of closed n--cycles in a strongly n--concave complex space has a natural structure of reduced complex space locally of finite dimension and represents the functor "analytic family of n--cycles" parametrized by banach analytic sets.
Simple strategies for Banach-Mazur games and fairly correct systems
Thomas Brihaye
2013-07-01
Full Text Available In 2006, Varacca and Völzer proved that on finite graphs, omega-regular large sets coincide with omega-regular sets of probability 1, by using the existence of positional strategies in the related Banach-Mazur games. Motivated by this result, we try to understand relations between sets of probability 1 and various notions of simple strategies (including those introduced in a recent paper of Grädel and Lessenich. Then, we introduce a generalisation of the classical Banach-Mazur game and in particular, a probabilistic version whose goal is to characterise sets of probability 1 (as classical Banach-Mazur games characterise large sets. We obtain a determinacy result for these games, when the winning set is a countable intersection of open sets.
Arens Regularity of Tensor Products and Weak Amenability of Banach Algebras
Azar, Kazem Haghnejad
2010-01-01
In this note, we study the Arens regularity of projective tensor product $A\\hat{\\otimes}B$ whenever $A$ and $B$ are Arens regular. We establish some new conditions for showing that the Banach algebras $A$ and $B$ are Arens regular if and only if $A\\hat{\\otimes}B$ is Arens regular. We also introduce some new concepts as left-weak$^*$-weak convergence property [$Lw^*wc-$property] and right-weak$^*$-weak convergence property [$Rw^*wc-$property] and for Banach algebra $A$, suppose that $A^*$ and $A^{**}$, respectively, have $Rw^*wc-$property and $Lw^*wc-$property. Then if $A^{**}$ is weakly amenable, it follows that $A$ is weakly amenable. We also offer some results concerning the relation between these properties with some special derivation $D:A\\rightarrow A^*$. We obtain some conclusions in the Arens regularity of Banach algebras.
Isometries of a function space
U. D. Vyas
1987-09-01
Full Text Available It is proved here that an isometry on the subset of all positive functions of L1âLp(â can be characterized by means of a function h together with a Borel measurable mapping Ï of â, thus generalizing the Banach-Lamparti theorem of Lp spaces.
Pelczynski's property (V) on spaces of vector valued functions
Randrianantoanina, N
1994-01-01
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
The Sociology of Lesbian and Gay Reflexivity or Reflexive Sociology?
Brian Heaphy
2008-01-01
This article is concerned with sociological conceptualisations of lesbian and gay sexualities as reflexive forms of existence, and identifies core problems with these. Our sociological narratives about lesbian and gay reflexivity tend to be partial in two senses. First, they talk about and envision only very particular - and relatively exclusive â€“ experience, and fail to adequately account for the significance of difference and power in shaping diverse lesbian and gay experiences. Second, t...
Some properties of space of compact operators
Randrianantoanina, N
1994-01-01
Let $X$ be a separable Banach space, $Y$ be a Banach space and $\\Lambda$ be a subset of the dual group of a given compact metrizable abelian group. We prove that if $X^*$ and $Y$ have the type I-$\\Lambda$-RNP (resp. type II-$\\Lambda$-RNP) then $K(X,Y)$ has the type I-$\\Lambda$-RNP (resp. type II-$\\Lambda$-RNP) provided $L(X,Y)=K(X,Y)$. Some corollaries are then presented as well as results conserning the separability assumption on $X$. Similar results for the NearRNP and the WeakRNP are also presented.
Management of Reflex Anoxic Seizures
J Gordon Millichap
2013-10-01
Full Text Available Investigators at the Roald Dahl EEG Unit, Alder Hey Children’s NHS Foundation, Liverpool, UK, review the definition, pathophysiology, clinical presentation, and management of reflex anoxic seizures (RAS in children.
Hoffmann reflex in idiopathic scoliosis.
Czernicki, Krzysztof; Dobosiewicz, Krystyna; Jedrzejewska, Anna; Durmala, Jacek
2006-01-01
This study was carried out in order to determine the dependence of selected Hoffmann reflex parameters on type, progression and morphology of idiopathic scoliosis (IS). Data collected from 129 girls with IS (59 progressive and 70 non-progressive cases) aged 7-16 years and 24 healthy subjects were analysed. H-reflex index (IH) and H/M amplitude index (IH/M) were calculated. Progressive left lumbar scoliosis expressed a significant decrease of IH values and a distinct tendency to IH/M depletion compared to non-progressives and controls. Progressive right thoracic scoliosis expressed marked tendency to IH decrease compared to nonprogressive scoliosis. No significant differences in H-reflex parameters were observed between the convex and concave side of the curvature or between types of scoliosis. H-reflex analysis in idiopathic scoliosis supports the hypothesis of a primary neurological disorder in progressive IS. PMID:17108418
Oculocardiac reflex during strabismus surgery
Mehryar Taghavi Gilani
2016-12-01
Full Text Available The activation of oculucardiac reflex (OCR is common during the strabismus surgeries. OCR is known as a trigemino-vagal reflex, which leads to the various side effects including bradycardia, tachycardia, arrhythmia, or in some cases cardiac arrest. This reflex could be activated during intraorbital injections, hematomas, and mechanical stimulation of eyeball and extraocular muscles surgeries. The incidence of OCR varies in a wide range, from 14% to 90%, that depends on anesthetic strategy and drug used for the surgery. The efficacy of various anticholinergic and anesthetic agents on declining the OCR reflex has been evaluated in different studies, especially in children. Although the detection of OCR goes back to 1908, its exact effect is not well recognized during strabismus surgery. In this review, we aimed to summarize the studies investigated the efficacy and potential of various anesthetic medications on inhibiting the OCR in children undergoing strabismus surgery.
Management of Reflex Anoxic Seizures
J. Gordon Millichap
2013-01-01
Investigators at the Roald Dahl EEG Unit, Alder Hey Children’s NHS Foundation, Liverpool, UK, review the definition, pathophysiology, clinical presentation, and management of reflex anoxic seizures (RAS) in children.
Weakly countably determined spaces of high complexity
Avilés, Antonio
2009-01-01
We prove that there exist weakly countably determined spaces of complexity higher than coanalytic. On the other hand, we also show that coanalytic sets can be characterized by the existence of a cofinal adequate family of closed sets. Therefore the Banach spaces constructed by means of these families have at most coanalytic complexity.
Spaces of continuous functions over Dugundji compacta
Banakh, Taras; Kubis, Wieslaw
2006-01-01
We show that for every Dugundji compact $K$ of weight aleph one the Banach space $C(K)$ is 1-Plichko and the space $P(K)$ of probability measures on $K$ is Valdivia compact. Combining this result with the existence of a non-Valdivia compact group, we answer a question of Kalenda.
The minimal displacement and extremal spaces
Bolibok, Krzysztof; Wi?nicki, Andrzej; Wo?ko, Jacek
2013-01-01
We show that both separable preduals of $L_{1}$ and non-type I $C^*$-algebras are strictly extremal with respect to the minimal displacement of $k$-Lipschitz mappings acting on the unit ball of a Banach space. In particular, every separable $C(K)$ space is strictly extremal.
SYSTEM REFLEXIVE STRATEGIC MARKETING MANAGEMENT
Andrii A. DLIGACH
2012-07-01
Full Text Available This article reviews the System Reflexive paradigm of strategic marketing management, being based on the alignment of strategic economic interests of stakeholders, specifically, enterprise owners and hired managers, and consumers. The essence of marketing concept of management comes under review, along with the strategic management approaches to business, buildup and alignment of economic interests of business stakeholders. A roadmap for resolving the problems of modern marketing is proposed through the adoption of System Reflexive marketing theory.
Reflexive fatherhood in everyday life
Westerling, Allan
2015-01-01
This article looks at fathering practices in Denmark, using the findings from a research project on everyday family life in Denmark. It takes a social psychological perspective and employs discursive psychology and theories about reflexive modernisation. It shows how fathers orient towards intimacy...... in their relationships with their children. Moreover, it discusses how fathers’ relatedness reflects individualisation and detraditionalisation. It is argued that reflexive modernisation entails subjective orientations that enable novel pathways to intimacy in contemporary father–child relationships...
Polynomial Bridgeland Stable Objects and Reflexive Sheaves
Lo, Jason
2011-01-01
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.
Dentocardiac Reflex: an Allegedly New Subform of the Trigeminocardiac Reflex
Amr Abdulazim
2011-05-01
Full Text Available Trigeminocardiac reflex (TCR is currently defined as a sudden bradycardia and decrease in mean arterial blood pressure by 20% during the manipulation of the branches of trigeminal nerve. TCR, especially during the last decade has been mostly studied in the course of neurosurgical procedures which are supposed to elicit the central subtype of TCR. Previously the well-known oculocardiac reflex was also considered as a subtype of TCR. Recently, surgeons dealing with the other branches of the fifth cranial nerve have become more interested in this reflex. Some noteworthy points have been published discussing new aspects of the trigeminocardiac reflex (TCR in simple oral surgical procedures. Arakeri et al. have reviewed the similarities and differences between TCR, vasovagal response (VVR, and syncope. They have also explained a new possible pathway for the reflex during the simple extraction of upper first molars. The present paper aims to briefly discuss these recently presented points. Although the discussed concepts are noteworthy and consistent our preliminary results of our yet to be published studies, it seemed timely for us to discuss some possible shortcomings that may affect the results of such assessments.
A Banach Algebra Approach To Amalgamated R- and S-transforms
Aagaard, L
2004-01-01
We give a Banach algebra approach to the additiveness property of Voiculescu's amalgamated R-transform. We also define an amalgamated S-transform and prove that it is multiplicative on products of amalgamated free random variables when the algebra of amalgamation is commutative.
Central limit theorem for the Banach-valued weakly dependent random variables
The central limit theorem (CLT) for the Banach-valued weakly dependent random variables is proved. In proving CLT convergence of finite-measured (i.e. cylindrical) distributions is established. A weak compactness of the family of measures generated by a certain sequence is confirmed. The continuity of the limiting field is checked
On solvability of some quadratic functional-integral equation in Banach algebra
Using the technique of a suitable measure of non-compactness in Banach algebra, we prove an existence theorem for some functional-integral equations which contain, as particular cases, a lot of integral and functional-integral equations that arise in many branches of nonlinear analysis and its applications. Also, the famous Chandrasekhar's integral equation is considered as a special case. (author)
Subspaces of almost Daugavet spaces
Lücking, Simon
2010-01-01
We study the almost Daugavet property, a generalization of the Daugavet property. It is analysed what kind of subspaces and sums of Banach spaces with the almost Daugavet property have this property as well. The main result of the paper is: if $Z$ is a closed subspace of a separable almost Daugavet space $X$ such that the quotient space $X/Z$ contains no copy of $\\ell_1$, then $Z$ has the almost Daugavet property, too.
Ludkovsky, S. V.
2001-01-01
Stochastic processes on totally disconnected topological groups are investigated. In particular they are considered for diffeomorphism groups and loop groups of manifolds on non-Archimedean Banach spaces. Theorems about a quasi-invariance and a pseudo-differentiability of transition measures are proved. Transition measures are used for the construction of strongly continuous representations including irreducible of these groups. In addition stochastic processes on general Banach-Lie groups, l...
Composition Operators on Laguerre-Cauchy Type Spaces
El-Bachir Yallaoui
2014-01-01
Full Text Available We study the action of the composition operators on the analytic function spaces whose kernels are special cases of Laguerre polynomials. These function spaces become Banach spaces when the kernels are integrated with respect to the complex Borel measures of the unit circle. Necessary and sufficient conditions for the composition operators to be compact are found.
On some interpolation properties in locally convex spaces
The aim of this paper is to introduce the notion of interpolation between locally convex spaces, the real method, and to present some elementary results in this setting. This represents a generalization from the Banach spaces framework to the locally convex spaces sequentially complete one, where the operators acting on them are locally bounded
On some interpolation properties in locally convex spaces
Pater, Flavius [Department of Mathematics, Politehnica University of Timi?oara, 300004 Timi?oara (Romania)
2015-03-10
The aim of this paper is to introduce the notion of interpolation between locally convex spaces, the real method, and to present some elementary results in this setting. This represents a generalization from the Banach spaces framework to the locally convex spaces sequentially complete one, where the operators acting on them are locally bounded.
Fixed Points of Non-expansive Operators on Weakly Cauchy Normed Spaces
Sahar M. Ali
2007-01-01
Full Text Available We proved the existence of fixed points of non-expansive operators defined on weakly Cauchy spaces in which parallelogram law holds, the given normed space is not necessarily be uniformly convex Banach space or Hilbert space, we reduced the completeness and the uniform convexity assumptions which imposed on the given normed space.
The Intuitionistic Fuzzy Normed Space of Coefficients
Bilalov, B.T.; Farahani, S. M.; F. A. Guliyeva
2012-01-01
Intuitionistic fuzzy normed space is defined using concepts of $t$ -norm and $t$ -conorm. The concepts of fuzzy completeness, fuzzy minimality, fuzzy biorthogonality, fuzzy basicity, and fuzzy space of coefficients are introduced. Strong completeness of fuzzy space of coefficients with regard to fuzzy norm and strong basicity of canonical system in this space are proved. Strong basicity criterion in fuzzy Banach space is presented in terms of coefficient operator.
[The oculocardiac reflex in blepharoplasties].
Rippmann, V; Scholz, T; Hellmann, S; Amini, P; Spilker, G
2008-08-01
The oculocardiac reflex (OCR) is a well-known phenomenon in ophthalmic surgery, but is rarely described in aesthetic blepharoplasty surgery. It was first mentioned in 1908 by Ascher and Dagnini. Since then, ophthalmologists and anaesthesiologists have regarded the onset of the oculocardiac reflex as a significant intraoperative problem, which is undermined by several case reports that describe dysrhythmias which have haved caused morbidity and death. Per definition the OCR is caused by ocular manipulation and involves intraoperative bradycardia by a change of 20 beats/minute compared to the preoperative heart rate or any dysrhythmia during the manipulation via a trigeminal-vagal-mediated reflex arc. Having operated on a 48-year-old, healthy woman in our clinic, who underwent a cardiac arrest during the blepharoplasty procedure, followed by a successful resuscitation, we investigated the onset of the OCR in our blepharoplasty patients within the last 3 years. The onset of the OCR was noted in 22 of 110 (20 %) blepharoplasty patients, mainly affecting younger, low-weighted patients operated under local anaesthesia. Awareness and treatment of this potentially life-threatening oculocardiac reflex are necessary. In most cases the onset of the reflex may be avoided by a gentle operation technique and by refraining from severe traction to the muscle or fat pad. The best treatment of a profound bradycardia caused by the OCR is to release tension to the muscle or fat pad in order to permit the heart rate to return to normal. Intraoperative monitoring is of utmost importance. PMID:18716987
Stochastic processes on non-Archimedean spaces. I. Stochastic processes on Banach spaces
Ludkovsky, S. V.
2001-01-01
Non-Archimedean analogs of Markov quasimeasures and stochastic processes are investigated. Thery are used for the development of stochastic antiderivations. The non-Archimedean analog of the It$\\hat o$ formula is proved.
A contribution to group representations in locally convex spaces
Let U be a continuous representation of a (connected) locally compact group G in a separated locally convex space E. It is shown that the study of U is equivalent to the study of a family Usub(i) of continuous representations of G in Frechet spaces Fsub(i). If U is equicontinuous, the Fsub(i) are Banach spaces, and the Usub(i) are realized by isomeric operators. When U is topologically irreducible, it is Naemark equivalent to a Frechet (or isomeric Banach, in the equicontinuous case) continuous representation. Similar results hold for semi-groups. (Auth.)
Survey on nonlocal games and operator space theory
Palazuelos, Carlos; Vidick, Thomas
2016-01-01
This review article is concerned with a recently uncovered connection between operator spaces, a noncommutative extension of Banach spaces, and quantum nonlocality, a striking phenomenon which underlies many of the applications of quantum mechanics to information theory, cryptography, and algorithms. Using the framework of nonlocal games, we relate measures of the nonlocality of quantum mechanics to certain norms in the Banach and operator space categories. We survey recent results that exploit this connection to derive large violations of Bell inequalities, study the complexity of the classical and quantum values of games and their relation to Grothendieck inequalities, and quantify the nonlocality of different classes of entangled states.
Survey on nonlocal games and operator space theory
This review article is concerned with a recently uncovered connection between operator spaces, a noncommutative extension of Banach spaces, and quantum nonlocality, a striking phenomenon which underlies many of the applications of quantum mechanics to information theory, cryptography, and algorithms. Using the framework of nonlocal games, we relate measures of the nonlocality of quantum mechanics to certain norms in the Banach and operator space categories. We survey recent results that exploit this connection to derive large violations of Bell inequalities, study the complexity of the classical and quantum values of games and their relation to Grothendieck inequalities, and quantify the nonlocality of different classes of entangled states
Survey on nonlocal games and operator space theory
Palazuelos, Carlos, E-mail: cpalazue@mat.ucm.es [Instituto de Ciencias Matemáticas (ICMAT), Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Madrid (Spain); Vidick, Thomas, E-mail: vidick@cms.caltech.edu [Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, California 91125 (United States)
2016-01-15
This review article is concerned with a recently uncovered connection between operator spaces, a noncommutative extension of Banach spaces, and quantum nonlocality, a striking phenomenon which underlies many of the applications of quantum mechanics to information theory, cryptography, and algorithms. Using the framework of nonlocal games, we relate measures of the nonlocality of quantum mechanics to certain norms in the Banach and operator space categories. We survey recent results that exploit this connection to derive large violations of Bell inequalities, study the complexity of the classical and quantum values of games and their relation to Grothendieck inequalities, and quantify the nonlocality of different classes of entangled states.
Complemented copies of $\\ell_{1}$ in spaces of vector valued measures and applications
Randrianantoanina, N
1995-01-01
Let $X$ be a Banach space and $(\\Omega,\\Sigma)$ be a measure space. We provide a characterization of sequences in the space of $X$-valued countably additive measures on $\\Omega,\\Sigma)$ of bounded variation that generate complemented copies of $\\ell_1$. As application, we prove that if a dual Banach space $E^*$ has Pe\\l czy\\'nski's property (V*) then so does the space of $E^*$-valued countably additive measures with bounded variation. Another application, we show that for a Banach space $X$, the space $\\ell_\\infty(X)$ contains a complemented copy of $\\ell_1$ if and only if $X$ contains all $\\ell_1^n$ uniformly complemented.
Two ways to support reflexivity
Adriansen, Hanne Kirstine; Knudsen, Hanne
2013-01-01
A current challenge to public managers is the lack of a well-defined role. How can master’s programmes prepare managers to live up to an undefined function? In this paper we argue that the lack of role description enhances the need for reflexivity and show how it is done at Master in Educational......’. This requires participants to conduct experiments in their own organization, to reflect on and analyse their experiences with concepts from the curriculum. While the new language and the experimental teaching format are difficult, the participants learn a reflexive practice that can enable them to life...... up to an undefined role....
2-Local derivations on matrix algebras over semi-prime Banach algebras and on AW*-algebras
Ayupov, Shavkat; Kudaybergenov, Karimbergen
2016-03-01
The paper is devoted to 2-local derivations on matrix algebras over unital semi-prime Banach algebras. For a unital semi-prime Banach algebra A with the inner derivation property we prove that any 2-local derivation on the algebra M 2n (A), n ≥ 2, is a derivation. We apply this result to AW*-algebras and show that any 2-local derivation on an arbitrary AW*-algebra is a derivation.
Sur la continuité automatique des épimorphismes dans les ☆-algèbres de Banach
Y. Tidli; Tajmouati, A.; Oukhtite, L.
2004-01-01
Nous étudions les problèmes de continuité automatique dans des algèbres de Banach avec involutions. Nous obtenons aussi des nouveoux résultats concernant ☆-idéals des ☆-algèbres.We study the automatic continuity problems for Banach algebras with involutions. We also obtain some new results concerning ☆-ideals of ☆-algebras.
Reflexivity and technology in adult learning
Neil Selwyn
2005-01-01
It is argued by influential commentators such as Ulrich Beck and Scott Lash that we now live in a ‘reflexively modern' age. People are seen to now be free of the structures of modern society and driven instead by individualised opportunities to reflexively engage with their fast-changing social worlds and identities. Taking the notion of reflexive modernisation as its starting point, this paper explores the roles that information technologies (ITs) may play in supporting adults' reflexive jud...
Educating the Reflexive Practitioner
Marc J. Neveu
2012-09-01
Full Text Available “I cannot teach anybody anything, I can only make them think.”SocratesIntroductionStudio as a model of education is distinct from many other professionaldisciplines and although it can be quite rewarding on many levels it mayalso be an extremely unconstructive endeavor.1 The amount of time spent in studio typically far outweighs that spent for other courses and often atthe expense of such other courses. The dedication that students bring tothe studio is remarkable, yet much of the time spent in studio is not alwaysproductive. Students often complain of not knowing what is expected ofthem and as a result much of the time is spent thinking about what they think the professor wants to see as opposed to working through theirprojects. In an alternate scenario, students are crushed by the workload, tasks, demands or expectations of their instructors. In either case, the work is almost invariably driven by the students’ own creativity and imagination; unlike law, medicine, business, or engineering for example, where the interpretation and inquiry into case studies and cadaversis much less based on the personal introspection than established traditions. This extremely personal nature of the architectural studio canmake reviews either a devastating or extremely empowering process. As seen from the perspective of the larger university community, the studio is simply not an efficient way of education. The faculty to student ratio, for example, is not in accordance with other undergraduate disciplines. But this ratio, as we all know can also be a real strength. The often hermeticnature of the studio offers latitude for students to develop theirwork in relatively safe surroundings. This environment, however, may also foster the cult of personality that develops around certain professorsthat harkens back to the very roots of education but can also lead to anentourage of disciples who have no incentive to inform the Emperor that he or she is no longer wearing any clothes.Notwithstanding such issues, I do believe the studio holds the potentialto be an empowering learning experience. The intention of this article is to question the mode of instruction in an architectural studio. I’ve structured the paper in three parts. First, I will briefly describe the findingsof the study made by the Carnegie Foundation for the Advancementof Teaching known as the Boyer Report.2 To develop and support the findings of the Boyer Report, I introduce the work of the educator Donald Schön. Though I see much merit in the Boyer Report, and Schön’sproposals, I argue that a more nuanced approach is required. I will recommend, therefore, in the second section of this paper that a meansof architectural education as based on the Socratic method may be amore productive approach. My reading of the Socratic method is basedprimarily on early Socratic dialogues and I will specifically use Charmidesto illustrate the issues that I believe are relevant to studio pedagogy.3 From my analysis of Charmides I will, in the third section of the essay,describe how the Socratic method is beneficial to studio pedagogy threeways: reflexive, non-propositional, and finally how Socrates’ approachmay indeed be practical. This last section will be illustrated with a studentproject. It is my conjecture that the Socratic method offers insight intocurrent discussions of educational theory, namely student-centered,project-based learning.
Tonic vibration reflexes and background force level
Lackner, James R.; Dizio, Paul; Fisk, John
1992-01-01
On earth, the functional stretch reflex is an important component in the maintenance of posture and muscle tone. In parabolic flight experiments, it is evaluated whether the functional stretch reflex, as reflected in the tonic vibration reflex, adjusts appropriately for changes in background gravitoinertial force level. Virtually immediate alterations of appropriate sign occurred.
Stereotype locally convex spaces
Akbarov, S. S.
2000-08-01
We give complete proofs of some previously announced results in the theory of stereotype (that is, reflexive in the sense of Pontryagin duality) locally convex spaces. These spaces have important applications in topological algebra and functional analysis.
Stereotype locally convex spaces
We give complete proofs of some previously announced results in the theory of stereotype (that is, reflexive in the sense of Pontryagin duality) locally convex spaces. These spaces have important applications in topological algebra and functional analysis
Stereotype locally convex spaces
Akbarov, S S
2000-08-31
We give complete proofs of some previously announced results in the theory of stereotype (that is, reflexive in the sense of Pontryagin duality) locally convex spaces. These spaces have important applications in topological algebra and functional analysis.
The reflexive case study method
Rittenhofer, Iris
2015-01-01
This paper extends the international business research on small to medium-sized enterprises (SME) at the nexus of globalization. Based on a conceptual synthesis across disciplines and theoretical perspectives, it offers management research a reflexive method for case study research of postnational...
Some properties of the noncommutative Hp(r ,s ) (𝒜; ??) and Hp(𝒜; ?1) spaces
Tulenov, Kanat
2015-09-01
In this paper, we introduce the noncommutative Hp(r ,s ) (𝒜; ??) and Hp (𝒜; ?1) spaces. Then, it is shown that both spaces are Banach spaces for r, s ? 2 (and resp. p ? 1) and the analogue of Saito's theorem for the Hp(r ,s ) (𝒜; ??) and Hp(𝒜; ?1) spaces are proved.
On the Banach algebra Ã¢Â„Â¬(lp(ÃŽÂ±
Bruno de Malafosse
2004-11-01
Full Text Available We give some properties of the Banach algebra of bounded operators Ã¢Â„Â¬(lp(ÃŽÂ± for 1Ã¢Â‰Â¤pÃ¢Â‰Â¤Ã¢ÂˆÂž, where lp(ÃŽÂ±=(1/ÃŽÂ±Ã¢ÂˆÂ’1Ã¢ÂˆÂ—lp. Then we deal with the continued fractions and give some properties of the operator ÃŽÂ”h for h>0 or integer greater than or equal to one mapping lp(ÃŽÂ± into itself for pÃ¢Â‰Â¥1 real. These results extend, among other things, those concerning the Banach algebra SÃŽÂ± and some results on the continued fractions.
Bessel and Grüss Type Inequalities in Inner Product Modules over Banach -Algebras
Dragomir SS
2011-01-01
Full Text Available We give an analogue of the Bessel inequality and we state a simple formulation of the Grüss type inequality in inner product -modules, which is a refinement of it. We obtain some further generalization of the Grüss type inequalities in inner product modules over proper -algebras and unital Banach -algebras for -seminorms and positive linear functionals.
Star product realizations of kappa-Minkowski space
Durhuus, Bergfinnur; Sitarz, Andrzej
2013-01-01
We define a family of star products and involutions associated with κ -Minkowski space. Applying corresponding quantization maps we show that these star products restricted to a certain space of Schwartz functions have isomorphic Banach algebra completions. For two particular star products it is...
Weighted norms and Volterra integral equations in LP spaces
Jaroslaw Kwapisz
1991-01-01
Full Text Available A new simple proof of existence and uniqueness of solutions of the Volterra integral equation in Lebesque spaces is given. It is shown that the weighted norm technique and the Banach contraction mapping principle can be applied (as in the case of continuous functions space.
ON STRONG AND WEAK CONVERGENCE IN n-HILBERT SPACES
Agus L. Soenjaya
2014-03-01
Full Text Available We discuss the concepts of strong and weak convergence in n-Hilbert spaces and study their properties. Some examples are given to illustrate the concepts. In particular, we prove an analogue of Banach-Saks-Mazur theorem and Radon-Riesz property in the case of n-Hilbert space.
Strong and Convergence Theorems for Multivalued Mappings in Spaces
Laowang W
2009-01-01
Full Text Available We show strong and convergence for Mann iteration of a multivalued nonexpansive mapping whose domain is a nonempty closed convex subset of a CAT(0 space. The results we obtain are analogs of Banach space results by Song and Wang [2009, 2008]. Strong convergence of Ishikawa iteration are also included.
Casazza, Peter G
1989-01-01
This monograph provides a structure theory for the increasingly important Banach space discovered by B.S. Tsirelson. The basic construction should be accessible to graduate students of functional analysis with a knowledge of the theory of Schauder bases, while topics of a more advanced nature are presented for the specialist. Bounded linear operators are studied through the use of finite-dimensional decompositions, and complemented subspaces are studied at length. A myriad of variant constructions are presented and explored, while open questions are broached in almost every chapter. Two appendices are attached: one dealing with a computer program which computes norms of finitely-supported vectors, while the other surveys recent work on weak Hilbert spaces (where a Tsirelson-type space provides an example).
Huai-Xin Cao
2009-01-01
Full Text Available 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 Δf,g1, Δf,g2, Δf,g3, and Δf,g4 are defined and it is proved that if ∥Δf,g1(x,y,z,w∥ (resp., ∥Δf,g3(x,y,z,w,α,β∥ is dominated by φ(x,y,z,w, then f is a generalized (resp., linear module-𝒜 left derivation and g is a (resp., linear module-X left derivation. It is also shown that if ∥Δf,g2(x,y,z,w∥ (resp., ∥Δf,g4(x,y,z,w,α,β∥ is dominated by φ(x,y,z,w, then f is a generalized (resp., linear module-𝒜 derivation and g is a (resp., linear module-X derivation.
On the L-characteristic of nonlinear superposition operators in lp-spaces
In this paper we describe the L-characteristic of the nonlinear superposition operator F(x) f(s,x(s)) between two Banach spaces of functions x from N to R. It was shown that L-characteristic of the nonlinear superposition operator which acts between two Lebesgue spaces has so-called Σ-convexity property. In this paper we show that L-characteristic of the operator F (between two Banach spaces) has the convexity property. It means that the classical interpolation theorem of Reisz-Thorin for a linear operator holds for the nonlinear operator superposition which acts between two Banach spaces of sequences. Moreover, we consider the growth function of the operator superposition in mentioned spaces and we show that one has the logarithmically convexity property. (author). 7 refs
A note on mutiplication operators on Köthe-Bochner spaces
S. S. Khurana
2012-02-01
Full Text Available Let (Ω, A, μ is a finite measure space, E an order continuous Banach function space over μ, X a Banach space and E(X the Köthe-Bochner space. A new simple proof is given of the result that a continuous linear operator T: E(X ® E(X is a multiplication operator (by a function in L¥ iff T(g f, x* > x =g T(f, x* > x for everyg Î L¥, f Î E(X, x Î X, x* Î X*.
Integrating Reflexivity in Livelihoods Research
Prowse, Martin
2010-01-01
Much poverty and development research is not explicit about its methodology or philosophical foundations. Based on the extended case method of Burawoy and the epistemological standpoint of critical realism, this paper discusses a methodological approach for reflexive inductive livelihoods researc...... that overcomes the unproductive social science dualism of positivism and social constructivism. The approach is linked to a conceptual framework and a menu of research methods that can be sequenced and iterated in light of research questions.......Much poverty and development research is not explicit about its methodology or philosophical foundations. Based on the extended case method of Burawoy and the epistemological standpoint of critical realism, this paper discusses a methodological approach for reflexive inductive livelihoods research...
Integrating Reflexivity in Livelihoods Research
Prowse, Martin
2010-01-01
Much poverty and development research is not explicit about its methodology or philosophical foundations. Based on the extended case method of Burawoy and the epistemological standpoint of critical realism, this paper discusses a methodological approach for reflexive inductive livelihoods research that overcomes the unproductive social science dualism of positivism and social constructivism. The approach is linked to a conceptual framework and a menu of research methods that can be sequenced ...
Reflexivity in Narratives on Practice
Jakobsen, Helle Nordentoft; Olesen, Lektor Birgitte Ravn
Previous research has shown how reflexivity is a precondition for knowledge co-production through productive dialogue in organisational contexts because it entails a re-ordering, re-arranging and re-designing of what one knows and therefore creates new angles of vision. In this paper, we draw on ...... have the potential to bring about productive learning in organizational contexts since they appear to stimulate participants’ relational engagement and reflexivity.......Previous research has shown how reflexivity is a precondition for knowledge co-production through productive dialogue in organisational contexts because it entails a re-ordering, re-arranging and re-designing of what one knows and therefore creates new angles of vision. In this paper, we draw on...... dialogic conception of practice as they entail a conceptual reframing of key elements in practice. In addition, the narratives expose a situational and relational, rather than normative, focus which allows for reflections on emotional and bodily experiences. In conclusion, we argue that practice narratives...
On the Carleman ultradifferentiable vectors of a scalar type spectral operator
Markin, Marat V.
2016-01-01
A description of the Carleman classes of vectors, in particular the Gevrey classes, of a scalar type spectral operator in a reflexive complex Banach space is shown to remain true without the reflexivity requirement. A similar nature description of the entire vectors of exponential type, known for a normal operator in a complex Hilbert space, is generalized to the case of a scalar type spectral operator in a complex Banach space.
Weak Precompactness in the Space of Vector-Valued Measures of Bounded Variation
Ghenciu, Ioana
2015-01-01
For a Banach space X and a measure space (Ω,Σ), let M(Ω,X) be the space of all X-valued countably additive measures on (Ω,Σ) of bounded variation, with the total variation norm. In this paper we give a characterization of weakly precompact subsets of M(Ω,X).
The near Radon-Nikodym property in Lebesgue-Bochner function spaces
Randrianantoanina, N; Randrianantoanina, Narcisse; Saab, Elias
1997-01-01
Let $X$ be a Banach space $E$ a K\\"othe function space that does not contain $c_0$. It is shown that the vector valued function space $E(X)$ has the Near Radon Nikodym property if and only if $X$ does.
Duality of Variable Exponent Triebel-Lizorkin and Besov Spaces
Noi, Takahiro
2012-01-01
We will prove the duality and reflexivity of variable exponent Triebel-Lizorkin and Besov spaces. It was shown by many authors that variable exponent Triebel-Lizorkin spaces coincide with variable exponent Bessel potential spaces, Sobolev spaces, and Lebesgue spaces when appropriate indices are chosen. In consequence of the results, these variable exponent function spaces are shown to be reflexive.
Avaliao dos reflexos espinhais em bezerros Spinal reflexes in calves
Alexandre Secorun Borges
1997-12-01
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.
The emergence of reflexive global labour law
Rogowski, Ralf
2015-01-01
The article introduces the main tenets of reflexive labour law and uses this perspective to interpret core trends in global labour law. It suggests a conceptual distinction between international and global labour law and identifies a transformation in the global labour law regime related to processes of reflexivity and constitutionalisation. The first part of the article analyses reflexivity within the International Labour Organization (ILO) in relation to its policy of defining labour standa...
Arakeri’s Reflex: an Alternative Pathway for Dento-Cardiac Reflex Mediated Syncope
Veena Arali; Shailaja Reddy; C.G Raghuram; Gururaj Arakeri
2010-01-01
Introduction: Dentocardiac reflex, a variant of trigeminocardiac reflex elicited specifically during tooth extraction procedures in den-tal/maxillofacial surgery and is believed to cause syncope with an afferent link mediated by posterior superior alveolar nerve. Another variant of trigeminocardiac reflex which is also of interest to the oral and maxillofacial surgeon is oculocardiac reflex which can be triggered by direct or indirect manipulation of eye globe or muscles around it.The hypothe...
On the Carleman classes of vectors of a scalar type spectral operator
Markin, Marat V.
2004-01-01
The Carleman classes of a scalar type spectral operator in a reflexive Banach space are characterized in terms of the operator's resolution of the identity. A theorem of the Paley-Wiener type is considered as an application.
On Presic Type Generalization of the Banach Contraction Mapping Principle
S. Presic
2007-10-01
Full Text Available Let (X, d be a metric space, k a positive integer and T a mapping of Xk into X. In this paper we proved that if T satisfies conditions (2.1 and (2.2 below, then there exists a unique x in X such that T(x, x,, x = x, This result generalizes the corresponding theorems of the second author [4], [5] and the theorem of Dhage [3].
Porosity Results for Sets of Strict Contractions on Geodesic Metric Spaces
Bargetz, Christian; Dymond, Michael; Reich, Simeon
2016-01-01
We consider a large class of geodesic metric spaces, including Banach spaces, hyperbolic spaces and geodesic $\\mathrm{CAT}(\\kappa)$-spaces, and investigate the space of nonexpansive mappings on either a convex or a star-shaped subset in these settings. We prove that the strict contractions form a negligible subset of this space in the sense that they form a $\\sigma$-porous subset. For separable metric spaces we show that a generic nonexpansive mapping has Lipschitz constant one at typical poi...
Lakshmi Narayan Mishra
2016-04-01
Full Text Available In the present manuscript, we prove some results concerning the existence of solutions for some nonlinear functional-integral equations which contains various integral and functional equations that considered in nonlinear analysis and its applications. By utilizing the techniques of noncompactness measures, we operate the fixed point theorems such as Darbo's theorem in Banach algebra concerning the estimate on the solutions. The results obtained in this paper extend and improve essentially some known results in the recent literature. We also provide an example of nonlinear functional-integral equation to show the ability of our main result.
Lattices generated by skeletons of reflexive polytopes
Haase, Christian; Nill, Benjamin
2005-01-01
Lattices generated by lattice points in skeletons of reflexive polytopes are essential in determining the fundamental group and integral cohomology of Calabi-Yau hypersurfaces. Here we prove that the lattice generated by all lattice points in a reflexive polytope is already generated by lattice points in codimension two faces. This answers a question of J. Morgan.
A Model of the Hoffmann Reflex
Ward, T.
2000-01-01
The Hoffman reflex which has applications in assessment of nervous system damage in stroke, spinal injury, Parkinson's disease and other conditions is studied here both practically and theoretically. Using recorded Hoffman reflex data a model is proposed that captures the qualitative behaviour of the phenomenon and allows investigation of how different waveform morphologies and patterns of recruitment can be related to underlying physiological variables.
Reflexivity: Towards a Theory of Lifelong Learning.
Edwards, Richard; Ranson, Stewart; Strain, Michael
2002-01-01
The current notion of lifelong learning in policy and practice is dominated by behaviorist, adaptive accumulation of skills and qualifications. An alternative is reflexive lifelong learning, developed through social learning networks within the context of dislocation and uncertainty. It involves the reflexive practices of metacognitive analysis
$L^p$-Spaces as Quasi *-Algebras
Bagarello, F.; C. Trapani
1994-01-01
The Banach space $L^p(X,\\mu)$, for $X$ a compact Hausdorff measure space, is considered as a special kind of quasi *-algebra (called CQ*-algebra) over the C*-algebra $C(X)$ of continuous functions on $X$. It is shown that, for $p \\geq 2$, $(L^p(X,\\mu), C(X))$ is *-semisimple (in a generalized sense). Some consequences of this fact are derived.
Widths of embeddings of 2-microlocal Besov spaces
Zhang, Shun
2011-01-01
We consider the asymptotic behaviour of the approximation, Gelfand and Kolmogorov numbers of compact embeddings between 2-microlocal Besov spaces with weights defined in terms of the distance to a $d$-set $U\\subset \\mathbb{R}^n$. The sharp estimates are shown in most cases, where the quasi-Banach setting is included.
Baudier, Florent Pierre
2013-01-01
We give the first lower bound on the $\\scr C(K)$-distortion of the class of separable Banach spaces, for $K$ a countable compact in the family $\\{ [0,\\omega],[0,\\omega\\cdot2],\\cdots, [0,\\omega^2], \\cdots, [0,\\omega^k\\cdot n],\\cdots,[0,\\omega^\\omega]\\}$.
Topological centers of module actions and cohomological groups of Banach Algebras
Azar, Kazem Azem Haghnejad
2010-01-01
In this paper, first we study some Arens regularity properties of module actions. Let $B$ be a Banach $A-bimodule$ and let ${Z}^\\ell_{B^{**}}(A^{**})$ and ${Z}^\\ell_{A^{**}}(B^{**})$ be the topological centers of the left module action $\\pi_\\ell:~A\\times B\\rightarrow B$ and the right module action $\\pi_r:~B\\times A\\rightarrow B$, respectively. We investigate some relationships between topological center of $A^{**}$, ${Z}_1({A^{**}})$ with respect to the first Arens product and topological centers of module actions ${Z}^\\ell_{B^{**}}(A^{**})$ and ${Z}^\\ell_{A^{**}}(B^{**})$. On the other hand, if $A$ has Mazure property and $B^{**}$ has the left $A^{**}-factorization$, then $Z^\\ell_{A^{**}}(B^{**})=B$, and so for a locally compact non-compact group $G$ with compact covering number $card(G)$, we have $Z^\\ell_{M(G)^{**}}{(L^1(G)^{**})}= {L^1(G)}$ and $Z^\\ell_{L^1(G)^{**}}{(M(G)^{**})}= {M(G)}$. By using the Arens regularity of module actions, we study some cohomological groups properties of Banach algebra and we...
Common fixed points in best approximation for Banach operator pairs with Ciric type I-contractions
Hussain, N.
2008-02-01
The common fixed point theorems, similar to those of Ciric [Lj.B. Ciric, On a common fixed point theorem of a Gregus type, Publ. Inst. Math. (Beograd) (N.S.) 49 (1991) 174-178; Lj.B. Ciric, On Diviccaro, Fisher and Sessa open questions, Arch. Math. (Brno) 29 (1993) 145-152; Lj.B. Ciric, On a generalization of Gregus fixed point theorem, Czechoslovak Math. J. 50 (2000) 449-458], Fisher and Sessa [B. Fisher, S. Sessa, On a fixed point theorem of Gregus, Internat. J. Math. Math. Sci. 9 (1986) 23-28], Jungck [G. Jungck, On a fixed point theorem of Fisher and Sessa, Internat. J. Math. Math. Sci. 13 (1990) 497-500] and Mukherjee and Verma [R.N. Mukherjee, V. Verma, A note on fixed point theorem of Gregus, Math. Japon. 33 (1988) 745-749], are proved for a Banach operator pair. As applications, common fixed point and approximation results for Banach operator pair satisfying Ciric type contractive conditions are obtained without the assumption of linearity or affinity of either T or I. Our results unify and generalize various known results to a more general class of noncommuting mappings.
In some symmetric spaces monotonicity properties can be reduced to the cone of rearrangements
Hudzik, H.; Kaczmarek, R.; Krbec, Miroslav
2016-01-01
Roč. 90, č. 1 (2016), s. 249-261. ISSN 0001-9054 Institutional support: RVO:67985840 Keywords : symmetric space s * K-monotone symmetric Banach space s * strict monotonicity * lower local uniform monotonicity Subject RIV: BA - General Mathematics Impact factor: 0.918, year: 2014 http://link.springer.com/article/10.1007%2Fs00010-015-0379-6
A Valdivia compact space with no $G_\\delta$ points and few nontrivial convergent sequences
Correa, Claudia; Daniel V. Tausk
2015-01-01
We give an example of a Valdivia compact space with no $G_\\delta$ points and no nontrivial convergent sequences in the complement of a dense $\\Sigma$-subset. The example is related to a problem concerning twisted sums of Banach spaces.
Fuzzy optimization for portfolio selection based on Embedding Theorem in Fuzzy Normed Linear Spaces
Solatikia Farnaz
2014-05-01
Full Text Available Background: This paper generalizes the results of Embedding problem of Fuzzy Number Space and its extension into a Fuzzy Banach Space C(? C(?, where C(? is the set of all real-valued continuous functions on an open set ?.
We consider the following problem: how can one apply the methods employed for describing the cohomology of algebras and based on the use of the A∞-structures of Stasheff to describe the cohomology of Banach algebras and locally convex algebras
The oculocardiac reflex in blepharoplasty surgery.
Matarasso, A
1989-02-01
The oculocardiac reflex (OCR), a previously undescribed phenomenon in aesthetic blepharoplasty surgery, involves intraoperative bradycardia exceeding 10 percent of the preoperative heart rate or any dysrhythmia during ocular manipulation. It is a trigeminal-vagal-mediated reflex arc. The oculocardiac reflex was noted to occur in 25 of 100 patients (25 percent) undergoing blepharoplasty. A data sheet designed and distributed for use in the operating room identified a reflex-prone patient (RPP) as a young, anxious female, with a cardiac history, operated on under light anesthesia with aggressive fat pad resection. The oculocardiac reflex was more likely to occur in a reflex-prone patient during traction on the medial fat pads and in the left eye. Despite anticipating the fatigue phenomenon in those patients who exhibited a profound bradycardia (35 to 40 beats per minute), it was necessary to release traction in order to permit the heart rate to return to normal. Awareness and treatment of this potentially life-threatening oculocardiac reflex are necessary. Careful patient surveillance and monitoring are mandatory. PMID:2911623
Reflexivity and technology in adult learning
Neil Selwyn
2005-03-01
Full Text Available It is argued by influential commentators such as Ulrich Beck and Scott Lash that we now live in a ‘reflexively modern' age. People are seen to now be free of the structures of modern society and driven instead by individualised opportunities to reflexively engage with their fast-changing social worlds and identities. Taking the notion of reflexive modernisation as its starting point, this paper explores the roles that information technologies (ITs may play in supporting adults' reflexive judgements about, and reflexive engagements with, education and learning. Through an analysis of interview data with 100 adults in the UK the paper finds that whilst a minority of interviewees were using ITs to support and inform reflexive engagementwith learning, the majority of individuals relayed little sign of technology-supported reflexivity when it came to their (nonengagement with education. For most people ITs were found, at best, to reinforce pre-established tendencies to ‘drift' through the formal education system. The paper concludes by considering the implications of these findings for ongoing efforts in developed countries to establish technology-supported ‘learning societies'.
On H–Dichotomy for Skew-Evolution Semiflows in Banach Spaces
Stoica Codruţa
2012-04-01
Full Text Available The aim of this paper is to define and characterize a particular case of dichotomy for skew-evolution semiflows, called the H–dichotomy, as a useful tool in describing the behaviors for the solutions of evolution equations that describe phenomena from engineering or economics. The paper emphasizes also other asymptotic properties, as ω–growth and ω–decay, H–stability and H–instability, as well as the classic concept of exponential dichotomy.
Zajicek, Ludek
2013-01-01
The classical Denjoy-Young-Saks theorem on Dini derivatives of arbitrary functions $f: \\R \\to \\R$ was extended by U.S. Haslam-Jones (1932) and A.J. Ward (1935) to arbitrary functions on $\\R^2$. This extension gives the strongest relation among upper and lower Hadamard directional derivatives $f^+_H (x,v)$, $f^-_H (x,v)$ ($v \\in X$) which holds almost everywhere for an arbitrary function $f:\\R^2\\to \\R$. Our main result extends the theorem of Haslam-Jones and Ward to functions on separable Bana...
On Milmanâs moduli for Banach spaces
Mariusz Szczepanik
2001-08-01
Full Text Available We show that infinite dimensional geometric moduli introduced by Milman are strongly related to nearly uniform convexity and nearly uniform smoothness. An application of those moduli to fixed point theory is given.
Compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions
Davood Alimohammadi
2014-10-01
Full Text Available We characterize compact composition operators on real Banachspaces of complex-valued bounded Lipschitz functions on metricspaces, not necessarily compact, with Lipschitz involutions anddetermine their spectra.
Mujica, J
1985-01-01
Problems arising from the study of holomorphic continuation and holomorphic approximation have been central in the development of complex analysis in finitely many variables, and constitute one of the most promising lines of research in infinite dimensional complex analysis. This book presents a unified view of these topics in both finite and infinite dimensions.
Bonnans, J. Frederic; Cominetti, Roberto
1994-01-01
Nous tudions la sensibilit du cot optimal et des solutions de problmes d'optimisation dans deux cas. Le premier est quand des multiplicateurs existent mais seule la condition suffisante d'optimalit faible est satisfaite. Le second cas est lorsque l'ensemble des multiplicateurs est vide.
K Balachandran; K Uchiyama
2000-05-01
In this paper we prove the existence of mild and strong solutions of a nonlinear integrodifferential equation of Sobolev type with nonlocal condition. The results are obtained by using semigroup theory and the Schauder fixed point theorem.
On the mild solutions of higher-order differential equations in Banach spaces
Nguyen Thanh Lan
2003-08-01
Full Text Available For the higher-order abstract differential equation u(n(t=Au(t+f(t, tÃ¢ÂˆÂˆÃ¢Â„Â, we give a new definition of mild solutions. We then characterize the regular admissibility of a translation-invariant subspace Ã¢Â„Â³ of BUC(Ã¢Â„Â,E with respect to the above-mentioned equation in terms of solvability of the operator equation AXÃ¢ÂˆÂ’XÃ°ÂÂ’ÂŸn=C. As applications, periodicity and almost periodicity of mild solutions are also proved.
2009-02-01
Full Text Available We give conditions for the parabolic evolution operator to be analytic with respect to a coefficient operator. We also show that the solution of a homogeneous parabolic evolution equation is analytic with respect to the coefficient operator and to the initial data. We apply our results to example that can not be studied by the standard methods.
The fixed point theorems of 1-set-contractive operators in Banach space
Wang Shuang
2011-01-01
Full Text Available Abstract In this paper, we obtain some new fixed point theorems and existence theorems of solutions for the equation Ax = μx using properties of strictly convex (concave function and theories of topological degree. Our results and methods are different from the corresponding ones announced by many others. MSC: 47H09, 47H10
Chang Shih-sen
2008-01-01
Full Text Available Abstract In this paper, a new implicit iteration process with errors for finite families of strictly asymptotically pseudocontractive mappings and nonexpansive mappings is introduced. By using the iterative process, some strong convergence theorems to approximating a common fixed point of strictly asymptotically pseudocontractive mappings and nonexpansive mappings are proved. The results presented in the paper are new which extend and improve some recent results of Osilike et al. (2007, Liu (1996, Osilike (2004, Su and Li (2006, Gu (2007, Xu and Ori (2001.
Mouffak Benchohra
2012-01-01
Full Text Available The aim of this paper is to investigate a class of boundary value problems for fractional differential equations involving nonlinear integral conditions. The main tool used in our considerations is the technique associated with measures of weak noncompactness.
2006-01-01
Full Text Available The aim of this paper is twofold. First, several basic mathematical concepts involved in the construction and study of Bregman type iterative algorithms are presented from a unified analytic perspective. Also, some gaps in the current knowledge about those concepts are filled in. Second, we employ existing results on total convexity, sequential consistency, uniform convexity and relative projections in order to define and study the convergence of a new Bregman type iterative method of solving operator equations.
Pengyu Chen; Jia Mu
2010-01-01
We use a monotone iterative method in the presence of lower and upper solutions to discuss the existence and uniqueness of mild solutions for the initial value problem $$displaylines{ u'(t)+Au(t)= f(t,u(t),Tu(t)),quad tin J,; t eq t_k,cr Delta u |_{t=t_k}=I_k(u(t_k)) ,quad k=1,2,dots ,m,cr u(0)=x_0, }$$ where $A:D(A)subset Eo E$ is a closed linear operator and $-A$ generates a strongly continuous semigroup $T(t)(tgeq 0)$ in $E$. Under wide monotonicity conditions and the non-compac...
[Research progress of rectoanal inhibitory reflex].
Yin, Shuhui; Zhao, Ke
2015-12-01
The understanding of rectoanal inhibitory reflex (RAIR) is progressing for the latest 100 years. From the discovery of its important role in diagnosis of Hirschsprung's disease to all aspects of its development, reflex pathways, neural regulation and physiological functions, there have been more in-depth explorations. It is now recognized that a number of other diseases also have a more specific performance of RAIR. It has become an important and indispensable part to anorectal manometry. Research progress of rectoanal inhibitory reflex is reviewed in this article. PMID:26704013
New Molecular Knowledge Towards the Trigemino-Cardiac Reflex as a Cerebral Oxygen-Conserving Reflex
Sandu, N.; Spiriev, T.; Lemaitre, F; Filis, A.; Schaller, B.
2010-01-01
The trigemino-cardiac reflex (TCR) represents the most powerful of the autonomous reflexes and is a subphenomenon in the group of the so-called “oxygen-conserving reflexes”. Within seconds after the initiation of such a reflex, there is a powerful and differentiated activation of the sympathetic system with subsequent elevation in regional cerebral blood flow (CBF), with no changes in the cerebral metabolic rate of oxygen (CMRO2) or in the cerebral metabolic rate of glucose (CMRglc). Such an ...
Star product realizations of kappa-Minkowski space
Durhuus, Bergfinnur; Sitarz, Andrzej
2011-01-01
We define a family of star products and involutions associated with $\\kappa$-Minkowski space. Applying corresponding quantization maps we show that these star products restricted to a certain space of Schwartz functions have isomorphic Banach algebra completions. For two particular star products it is demonstrated that they can be extended to a class of polynomially bounded smooth functions allowing a realization of the full Hopf algebra structure on $\\kappa$-Minkowski space. Furthermore, we ...
Entrepreneurship Teaching Conducted as Strategic Reflexive Conversation
Kristiansson, Michael
The paper intends exploring and ascertaining whether the concept of strategic reflexive conversation can profitably be applied to entrepreneurship. As a start, a process of conceptualisation is undertaken, which is instrumental in placing the notion of strategic reflexive conversation into a...... knowledge management perspective. Strategic reflexive conversation is presented in an enhanced and updated version, which is contrasted to entrepreneurship through reflection. The findings indicate and it can be concluded that, with some important reservations, strategic reflexive conversation can...... advantageously, and on a pilot basis, be applied to entrepreneurship in practical environments and within the framework of entrepreneurship-centred teaching. The present theoretical investigation is solely of an introductory nature and steps are considered that can lead to the planning of additional exploratory...
The Multiple Faces of Reflexive Research Designs
Müller, Karl H.
2015-01-01
Reflexive research can be grouped into five clusters with circular relations between two elements x ↔ x, namely circular relations between observers, between scientific building blocks like concepts, theories or models, between systemic levels, between rules and rule systems or as circular relations or x ↔ y between these four components. By far the most important cluster is the second cluster which becomes reflexive through a re-entry operation RE into a scientific element x and which establ...
Weighted composition operators between weak spaces of vector-valued analytic functions
Hassanlou, Mostafa; Laitila, Jussi; VAEZI, Hamid
2014-01-01
We consider weighted composition operators on spaces of analytic functions on the unit disc, which take values in some complex Banach space. We provide necessary and sufficient conditions for the boundedness and (weak) compactness of weighted composition operators on general function spaces, and in particular on weak vector-valued spaces. As an application, we characterize the weak compactness of these operators between two different vector-valued Bloch-type spaces. This result appears to be ...
Infinitesimally Lipschitz functions on metric spaces
Durand-Cartagena, Estibalitz; Jaramillo Aguado, Jesús Ángel
2013-01-01
For a metric space $X$, we study the space $D^{\\infty}(X)$ of bounded functions on $X$ whose infinitesimal Lipschitz constant is uniformly bounded. $D^{\\infty}(X)$ is compared with the space $\\LIP^{\\infty}(X)$ of bounded Lipschitz functions on $X$, in terms of different properties regarding the geometry of $X$. We also obtain a Banach-Stone theorem in this context. In the case of a metric measure space, we also compare $D^{\\infty}(X)$ with the Newtonian-Sobolev space $N^{1, \\infty}(X)$. In pa...
The passive of reflexive verbs in Icelandic
Hlíf Árnadóttir
2011-10-01
Full Text Available 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, termed the Passive Acceptability Hierarchy. The validity of this hierarchy is confirmed by our diachronic corpus study of open access digital library texts from Icelandic journals and newspapers dating from the 19th and 20th centuries (tímarit.is. Finally, we sketch an analysis of the Reflexive Passive, proposing that the different acceptability rates of the Reflexive and New Passives lie in the argument status of the object. Simplex reflexive pronouns are semantically dependent on the verbs which select them, and should therefore be analyzed as syntactic arguments only, and not as semantic arguments of these verbs.
Next generation control system for reflexive aerostructures
Maddux, Michael R.; Meents, Elizabeth P.; Barnell, Thomas J.; Cable, Kristin M.; Hemmelgarn, Christopher; Margraf, Thomas W.; Havens, Ernie
2010-04-01
Cornerstone Research Group Inc. (CRG) has developed and demonstrated a composite structural solution called reflexive composites for aerospace applications featuring CRG's healable shape memory polymer (SMP) matrix. In reflexive composites, an integrated structural health monitoring (SHM) system autonomously monitors the structural health of composite aerospace structures, while integrated intelligent controls monitor data from the SHM system to characterize damage and initiate healing when damage is detected. Development of next generation intelligent controls for reflexive composites were initiated for the purpose of integrating prognostic health monitoring capabilities into the reflexive composite structural solution. Initial efforts involved data generation through physical inspections and mechanical testing. Compression after impact (CAI) testing was conducted on composite-reinforced shape memory polymer samples to induce damage and investigate the effectiveness of matrix healing on mechanical performance. Non-destructive evaluation (NDE) techniques were employed to observe and characterize material damage. Restoration of mechanical performance was demonstrated through healing, while NDE data showed location and size of damage and verified mitigation of damage post-healing. Data generated was used in the development of next generation reflexive controls software. Data output from the intelligent controls could serve as input to Integrated Vehicle Health Management (IVHM) systems and Integrated Resilient Aircraft Controls (IRAC). Reflexive composite technology has the ability to reduce maintenance required on composite structures through healing, offering potential to significantly extend service life of aerospace vehicles and reduce operating and lifecycle costs.
Ferro, Leonardo
2013-01-01
El objetivo principal de esta disertación es el estudio de la teoría de las álgebras de Lie–Jordan Banach y su papel en el marco de la mecánica clásica y cuántica y sus aplicaciones en diferentes ámbitos de las matemáticas. La investigación algebraica de los fundamentos de la física surgió de la búsqueda de una formulación “excepcional” para la mecánica cuántica, que finalmente culminó en la formulación de las álgebras de Jordan y las posteriores C∗–álgebras.............
Dinda, Bivas; T. K. SAMANTA; Jebril, Iqbal H.
2011-01-01
In this paper intuitionistic fuzzy {\\psi}-{\\phi}-contractive mappings are introduced. Intuitionistic fuzzy Banach contraction theorem for M-complete non-Archimedean intuitionistic fuzzy metric spaces and intuitionistic fuzzy Elelstein contraction theorem for non-Archimedean intuitionistic fuzzy metric spaces by intuitionistic fuzzy {\\psi}-{\\phi}-contractive mappings are proved.
Moduli of convexity and smoothness of reflexive subspaces of L^1
Lajara, S.; Pallares, A.; Troyanski, S.
2011-01-01
We show that for any probability measure \\mu there exists an equivalent norm on the space L^1(\\mu) whose restriction to each reflexive subspace is uniformly smooth and uniformly convex, with modulus of convexity of power type 2. This renorming provides also an estimate for the corresponding modulus of smoothness of such subspaces.
The trigeminocardiac reflex – a comparison with the diving reflex in humans
Lemaitre, Frederic; Schaller, Bernhard
2015-01-01
The trigeminocardiac reflex (TCR) has previously been described in the literature as a reflexive response of bradycardia, hypotension, and gastric hypermotility seen upon mechanical stimulation in the distribution of the trigeminal nerve. The diving reflex (DR) in humans is characterized by breath-holding, slowing of the heart rate, reduction of limb blood flow and a gradual rise in the mean arterial blood pressure. Although the two reflexes share many similarities, their relationship and especially their functional purpose in humans have yet to be fully elucidated. In the present review, we have tried to integrate and elaborate these two phenomena into a unified physiological concept. Assuming that the TCR and the DR are closely linked functionally and phylogenetically, we have also highlighted the significance of these reflexes in humans. PMID:25995761
Common subspaces of $L_{p}$-spaces
Koldobsky, A B
1992-01-01
For $n\\geq 2, p2,$ does there exist an $n$-dimensional Banach space different from Hilbert spaces which is isometric to subspaces of both $L_{p}$ and $L_{q}$? Generalizing the construction from the paper "Zonoids whose polars are zonoids" by R.Schneider we give examples of such spaces. Moreover, for any compact subset $Q$ of $(0,\\infty)\\setminus \\{2k, k\\in N\\},$ we can construct a space isometric to subspaces of $L_{q}$ for all $q\\in Q$ simultaneously. This paper requires vanilla.sty
Generalized Kӧthe $p$-dual spaces
Galdames Bravo, O.
2014-01-01
Let us consider a Banach function space $X$. The Kӧthe dual space can be characterized as the space of multipliers from $X$ to $L^1$. We extend this characterization to the space of multipliers from $X$ to $L^p$ in order to define the Kӧthe $p$-dual space of $X$. We analyze the properties of this space so as to use it as a tool for studying $p$-th power factorable operators. In particular, we compute $q$-concavity for these spaces and type and cotype when $X$ is an AM-spa...
Automorphisms in spaces of continuous functions on Valdivia compacta
Avilés, Antonio
2009-01-01
We show that there are no automorphic Banach spaces of the form C(K) with K continuous image of Valdivia compact except the spaces c0(I). Nevertheless, when K is an Eberlein compact of finite height such that C(K) is not isomorphic to c0(I), all isomorphism between subspaces of C(K) of size less than aleph_omega extend to automorphisms of C(K).
Snakes and articulated arms in an Hilbert space
Pelletier, Fernand
2011-01-01
The purpose of this paper is to give an illustration of results on integrability of distributions and orbits of vector fields on Banach manifolds obtained in [Pe] and [LaPe]. Using arguments and results of these papers, in the context of a separable Hilbert space, we give a generalization of a Theorem of accessibility contained in [Ha], [Ro] and proved for a finite dimensional Hilbert space
Stochastic processes on non-Archimedean spaces. II. Stochastic antiderivational equations
Ludkovsky, S. V.
2001-01-01
Stochastic antiderivational equations on Banach spaces over local non-Archimedean fields are investigated. Theorems about existence and uniqiuness of the solutions are proved under definite conditions. In particular Wiener processes are considered in relation with the non-Archimedean analog of the Gaussian measure.
Elena, Miroshnikova
2014-12-01
In weighted space Lp (Rn,?), 1 < p < ?, a new broad class of integral operators with anisotropically homogeneous kernels is investigated. For such operators boundedness theorem is proved. Also the Banach algebra generated by operators with anisotropically homogeneous kernels of compact type is considered. For elements of the algebra symbolic calculation is constructed, the invertibility criterion is obtained in terms of operator symbol.
An improvement of dimension-free Sobolev imbeddings in r spaces
Fiorenza, A.; Krbec, Miroslav; Schmeisser, H.-J.
2014-01-01
Roč. 267, č. 1 (2014), s. 243-261. ISSN 0022-1236 R&D Projects: GA ČR GAP201/10/1920 Institutional support: RVO:67985840 Keywords : imbedding theorem * small Lebesgue space * rearrangement-invariant Banach Subject RIV: BA - General Mathematics Impact factor: 1.322, year: 2014 http://www.sciencedirect.com/science/article/pii/S0022123614001724
Gelfand and Kolmogorov numbers of Sobolev embeddings of weighted function spaces II
Zhang, Shun
2011-01-01
We determine the sharp asymptotic degree of the Gelfand and Kolmogorov numbers of compact embeddings between weighted function spaces of Besov and Triebel-Lizorkin type with polynomial weights in the non-limiting case. This complements our previous results in the context of the quasi-Banach setting, $0 < p, q \\le \\infty$. In addition the comparisons with corresponding approximation numbers are made.
Reflexive structures an introduction to computability theory
Sanchis, Luis E
1988-01-01
Reflexive Structures: An Introduction to Computability Theory is concerned with the foundations of the theory of recursive functions. The approach taken presents the fundamental structures in a fairly general setting, but avoiding the introduction of abstract axiomatic domains. Natural numbers and numerical functions are considered exclusively, which results in a concrete theory conceptually organized around Church's thesis. The book develops the important structures in recursive function theory: closure properties, reflexivity, enumeration, and hyperenumeration. Of particular interest is the treatment of recursion, which is considered from two different points of view: via the minimal fixed point theory of continuous transformations, and via the well known stack algorithm. Reflexive Structures is intended as an introduction to the general theory of computability. It can be used as a text or reference in senior undergraduate and first year graduate level classes in computer science or mathematics.
Intrathecal baclofen and the H-reflex.
Macdonell, R A; Talalla, A; SWASH, M.; D.Grundy
1989-01-01
Baclofen was given intrathecally to six patients with severe lower limb spasticity due to traumatic spinal cord injury. The effects of the drug on spasticity and the ratio between the maximum amplitude of the H reflex and the M response from the soleus (Hmax/Mmax ratio) were assessed. In each patient, spasticity was reduced following intrathecal baclofen and in four patients there was a reduction in the amplitude of the H reflex and Hmax/Mmax ratio. These results suggest that the Hmax/Mmax ra...
Reflex control for safe autonomous robot operation
This paper describes the design of an autonomous, sonar-based world mapping system for collision prevention in robotic systems. Obstacle detection and mapping is performed as a task that competes with higher-level tasks for the robot's attention. All tasks are integrated within a hierarchy, organized and co-ordinated by schemes analogous to biological reflexes and fixed action patterns. It is illustrated how the existence of low-level reflex behaviours can enhance the survivability and autonomy of complex systems and simplify the design of complex higher-level controls like our autonomous sonar-based world mapping system
The Reflexive Teacher Educator in TESOL Roots and Wings
Edge, Julian
2010-01-01
Edge explores the construct of reflexivity in teacher education, differentiating it from, while locating it in, reflective practice, and introduces a framework (Copying, Applying, Theorising, Reflecting, Acting) to help teacher educators become reflexive professionals.
Unconditionally convergent series in the space C(Q)
Let B be a Banach space and B* its dual Banach space. B contains csub(0) (B does not contain csub(0)) if B contains (does not contain) a subspace isomorphic to the space csub(0) of sequences of numbers tending to zero. The series ?sub(n=1)sup(infinity) xsub(n) of elements of B is weakly unconditionally convergent (w.u.c.) iff ?sub(n=1)sup(infinity)|x*(xsub(n))| 0. Series of elements of C(Q) are considered here. Subspaces of C(Q) isomorphic to c0 are constructed, and criteria for a series of elements of C(Q) to be w.u.c. or u.c. are given. Finally, an improved theorem of giving characterizations of the elements of subalgebras of C(Q) not containing c0 is presented
Nasal Reflexes: Implications for Exercise, Breathing, and Sex
James N. BARANIUK; Merck, Samantha J.
2008-01-01
Nasal patency, with both congestion and decongestion, is affected in a wide variety of reflexes. Stimuli that lead to nasal reflexes include exercise, alterations of body position, pressure, and temperature, neurological syndromes, and dentists. As anticipated, the vagal and trigeminal systems are closely integrated through nasobronchial and bronchonasal reflexes. However, perhaps of greater pathophysiological importance are the naso-hypopharyngea-laryngeal reflexes that become aggravated dur...
Anatomy and neuro-pathophysiology of the cough reflex arc
Polverino Mario; Polverino Francesca; Fasolino Marco; Andò Filippo; Alfieri Antonio; De Blasio Francesco
2012-01-01
Abstract Coughing is an important defensive reflex that occurs through the stimulation of a complex reflex arc. It accounts for a significant number of consultations both at the level of general practitioner and of respiratory specialists. In this review we first analyze the cough reflex under normal conditions; then we analyze the anatomy and the neuro-pathophysiology of the cough reflex arc. The aim of this review is to provide the anatomic and pathophysiologic elements of evaluation of the...
Coorbit description and atomic decomposition of Besov spaces
Christensen, Jens Gerlach; Olafsson, Gestur
2011-01-01
Function spaces are central topic in analysis. Often those spaces and related analysis involves symmetries in form of an action of a Lie group. Coorbit theory as introduced by Feichtinger and Gr\\"ochenig and then later extended in [3] gives a unified method to construct Banach spaces of functions based on representations of Lie groups. In this article we identify the homogeneous Besov spaces on stratified Lie groups introduced in [13] as coorbit spaces in the sense of [3] and use this to derive atomic decompositions for the Besov spaces.
Reflexive Planning as Design and Work
Lissandrello, Enza; Grin, John
2011-01-01
In recent years, planning theorists have advanced various interpretations of the notion of reflexivity, inspired by American pragmatism, complexity theory, hermeneutics, discursive and collaborative planning. Scholars agree that “reflexivity” has a strong temporal dimension: it not only aims to...
Dilemmas and Deliberations in Reflexive Ethnographic Research
Robinson, Janean Valerie
2014-01-01
This paper traces insights into the challenges and dilemmas experienced whilst researching students' interpretations and understandings of the Behaviour Management in Schools policy in Western Australia. Journal records, supported by student transcripts, are woven together in a reflexive ethnographic journey--from the beginning phase of…
Biological Motion Cues Trigger Reflexive Attentional Orienting
Shi, Jinfu; Weng, Xuchu; He, Sheng; Jiang, Yi
2010-01-01
The human visual system is extremely sensitive to biological signals around us. In the current study, we demonstrate that biological motion walking direction can induce robust reflexive attentional orienting. Following a brief presentation of a central point-light walker walking towards either the left or right direction, observers' performance…
Atropine treatment of reflex anoxic seizures.
McWilliam, R C; Stephenson, J B
1984-01-01
In 7 children with unusually severe or frequent reflex anoxic seizures atropine treatment, which was well tolerated, reduced seizure frequency by a mean value of 98%. Treatment withdrawal (five patients) was followed by an increase in seizure frequency and reintroduction (three patients) by restoration of control.
Self hypnotherapeutic treatment of habitual reflex vomiting.
Sokel, B S; Devane, S P; Bentovim, A; Milla, P. J.
1990-01-01
A 9 year old boy with intractable postprandial reflex vomiting was taught a self hypnotherapy technique incorporating relaxation exercises, mental imagery, and suggestions of symptom relief. The sequence was recorded on a personal stereo cassette tape. Vomiting was completely eliminated within four weeks. At 12 month review vomiting had not recurred.
A reflexive perspective in problem solving
Chio, José Angel
2013-01-01
Full Text Available The objective of this paper is to favour the methodological process of reflexive analysis in problem solving in the general teaching methods that concentrates in strengthening the dimensional analysis, to gain a greater preparation of the students for the solution of mathematical problems.
Vestibulospinal control of reflex and voluntary head movement
Boyle, R.; Peterson, B. W. (Principal Investigator)
2001-01-01
Secondary canal-related vestibulospinal neurons respond to an externally applied movement of the head in the form of a firing rate modulation that encodes the angular velocity of the movement, and reflects in large part the input "head velocity in space" signal carried by the semicircular canal afferents. In addition to the head velocity signal, the vestibulospinal neurons can carry a more processed signal that includes eye position or eye velocity, or both (see Boyle on ref. list). To understand the control signals used by the central vestibular pathways in the generation of reflex head stabilization, such as the vestibulocollic reflex (VCR), and the maintenance of head posture, it is essential to record directly from identified vestibulospinal neurons projecting to the cervical spinal segments in the alert animal. The present report discusses two key features of the primate vestibulospinal system. First, the termination morphology of vestibulospinal axons in the cervical segments of the spinal cord is described to lay the structural basis of vestibulospinal control of head/neck posture and movement. And second, the head movement signal content carried by the same class of secondary vestibulospinal neurons during the actual execution of the VCR and during self-generated, or active, rapid head movements is presented.
Feminist Politics as Reflexive Citizenship
Nikos Katrivesis
2008-11-01
Full Text Available This article examines the potential feminist contribution to a radically renovated citizenship, according to which we all ought to undertake our responsibilities towards family, society and world. This contribution mainly consists in the critical transgression of the traditional dualism between private and public space, which arises from the politicization of everyday experience and results to the emergence of an essentially participial civil society.
Functional calculus on real interpolation spaces for generators of $C_{0}$-groups
Haase, Markus; Rozendaal, Jan
2014-01-01
We study functional calculus properties of $C_{0}$-groups on real interpolation spaces, using transference principles. We obtain interpolation versions of the classical transference principle for bounded groups and of a recent transference principle for unbounded groups. Then we show that each group generator on a Banach space has a bounded $H^{\\infty}_{1}$-calculus on real interpolation spaces. Additional results are derived from this.
Yanlai Chen; Tingqiu Cao; Baoxia Qin
2015-01-01
The authors discuss multiple solutions for the nth-order singular boundary value problems of nonlinear integrodifferential equations in Banach spaces by means of the fixed point theorem of cone expansion and compression. An example for infinite system of scalar third-order singular nonlinear integrodifferential equations is offered.
Fixed point theory in distance spaces
Kirk, William
2014-01-01
This is a monograph on fixed point theory, covering the purely metric aspects of the theoryparticularly results that do not depend on any algebraic structure of the underlying space. Traditionally, a large body of metric fixed point theory has been couched in a functional analytic framework. This aspect of the theory has been written about extensively. There are four classical fixed point theorems against which metric extensions are usually checked. These are, respectively, the Banach contraction mapping principal, Nadlers well known set-valued extension of that theorem, the extension of Banachs theorem to nonexpansive mappings, and Caristis theorem. These comparisons form a significant component of this book. This book is divided into three parts. Part I contains some aspects of the purely metric theory, especially Caristis theorem and a few of its many extensions. There is also a discussion of nonexpansive mappings, viewed in the context of logical foundations. Part I also contains certain re...
Coorbit description and atomic decomposition of Besov spaces
Christensen, Jens Gerlach; Mayeli, Azita; Olafsson, Gestur
2011-01-01
Function spaces are central topic in analysis. Often those spaces and related analysis involves symmetries in form of an action of a Lie group. Coorbit theory as introduced by Feichtinger and Gr\\"ochenig and then later extended in [3] gives a unified method to construct Banach spaces of functions based on representations of Lie groups. In this article we identify the homogeneous Besov spaces on stratified Lie groups introduced in [13] as coorbit spaces in the sense of [3] and use this to deri...