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

In this paper, we first show that there are some gaps in the fixed point theorems for fuzzy non-expansive mappings which are proved by Bag and Samanta, in [Bag T, Samanta SK. Fixed point theorems on fuzzy normed linear spaces. Inf Sci 2006;176:2910-31; Bag T, Samanta SK. Some fixed point theorems in fuzzy normed linear spaces. Inform Sci 2007;177(3):3271-89]. By introducing the notion of fuzzy and ?- fuzzy reflexiveBanachspaces, 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.

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

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

We show that the classes of separable reflexiveBanachspaces and of spaces with separable dual are strongly bounded. This gives a new proof of a recent result of E. Odell and Th. Schlumprecht, asserting that there exists a separable reflexiveBanachspace containing isomorphic copies of every separable uniformly convex Banachspaces.

The problems related to renorming of Banachspaces are in the heart of the theory of Banachspaces. These are more than fifty years old and play a key role in the development of the Banachspace theory. Our aim is to review of results on renorming, to present a history of the subject, and to introduce some open problems. We start with simple observations concerning definition and properties of Banachspaces.

We describe a construction of wavelets (coherent states) in Banachspaces generated by ``admissible'' group representations. Our main targets are applications in pure mathematics while connections with quantum mechanics are mentioned. As an example we consider operator valued Segal-Bargmann type spaces and the Weyl functional calculus. Keywords: Wavelets, coherent states, Banachspaces, group representations, covariant, contravariant (Wick) symbols, Heisenberg group, Segal-Bargmann spaces, Weyl functional calculus (quantization), second quantization, bosonic field.

[en] Banach algebra structures on the topological dual X* of a Banachspace 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 Banachspace X, different products, each of which turns X** into an associative Banach algebra which satisfies similar properties are also defined. 13 refs

In this paper we first take a detail survey of the study of the Banach-Saks property of Banachspaces and then show the Banach-Saks property of the product spaces generated by a finite number of Banachspaces having the Banach-Saks property. A more general inequality for integrals of a class of composite functions is also given by using this property.

We show that if $X$ is a Banachspace with a Schauder basis, $\\Omega\\subset X$ is a pseudoconvex open subset, and $u:\\,\\Omega\\to(-\\infty,\\infty)$ is a locally bounded function, then there are a Banachspace $Z$ and a holomorphic function $h:\\,\\Omega\\to Z$ with $u(x)<\\|h(x)\\|$ for all $x\\in\\Omega$.

We obtain sharp approximation results for into nearisometries between Lp spaces and nearisometries into a Hilbert space. Our main theorem is the optimal approximation result for nearsurjective nearisometries between general Banachspaces.

In this paper, we report on new results related to the existence of an adjoint for operators on separable Banachspaces 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 Banachspaces. Our third application provides a natural extension of the Schatten-class of operators to all separable Banachspaces. As a part of this program, we introduce a new class of separable Banachspaces. As a side benefit, these spaces also provide a natural framework for the (rigorous) construction of the path integral as envisioned by Feynman.

We explore the convergence of Kergin interpolation polynomials of holomorphic functions in Banachspaces, which need not be of bounded type. We also investigate a case where the Kergin series diverges.

This paper is devoted to the question "Under what conditions on a Banachspace E is it true that the bounded weak topology is locally convex?". The theorem of Banach and Dieudonné shows that reflexivity is a sufficient condition. The author proves that reflexivity is also a necessary condition

This paper studies Schauder frames in Banachspaces, a concept which is a natural generalization of frames in Hilbert spaces and Schauder bases in Banachspaces. 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 extend his characterization of the reflexivity of spaces with unconditional bases to spaces with unconditional frames.

Full Text Available Notes of the Problem Session which has been held on the section of BanachSpaces during the International conference dedicated to the 120-th anniversary of Stefan Banach in Lviv (Ukraine), September 17–21, 2012.

On every real Banachspace X we introduce a locally convex topology tau(p), canonically associated to the weak-polynomial topology w(P). It is proved that tau(p) is the finest locally convex topology on X which is coarser than w(P). Furthermore, the convergence of sequences is considered, and suffic...

Garrido Carballo, M. Isabel; Jaramillo Aguado, Jesus Angel; Llavona, José G.

A Banachspace $X$ with a Schauder basis is defined to have the restricted quotient hereditarily indecomposable (QHI) property if $X/Y$ is hereditarily indecomposable (HI) for any infinite codimensional subspace $Y$ with a successive finite-dimensional decomposition on the basis of $X$. A reflexivespace with the restricted QHI property is in particular HI, has HI dual, and is saturated with subspaces which are HI and have HI dual. The following dichotomy theorem is proved: any infinite dimensional Banachspace contains a quotient of subspace which either has an unconditional basis, or has the restricted QHI property.

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 Banachspace setting would be closer to reality. Furthermore, sparsity constraints using general Lp-norms or the B

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

We show that, as conjectured by Adrien Douady back in 1972, every complete metric space is homeomorphic (moreover, isometric) to the locus of zeros of an analytic map between two Banachspaces. As a corollary, a paracompact topological space admits the structure of a Banach analytic space if and only if it is metrizable with a complete metric. -- AmS TeX 2.1 source file. Research Report RP-94-144, Victoria Univ of Wellington, June 1994, 5 pp.

Full Text Available Let X be a Banachspace and S ( X ) = { x ? X , ? x ? = 1 } be the unit sphere of X . Parameters E ( X ) = sup ? { ? ( x ) , x ? S ( X ) } , e ( X ) = inf ? { ? ( x ) , x ? S ( X ) } , F ( X ) = sup ? { ? ( x ) , x ? S ( X ) } , and f ( X ) = inf ? { ? ( x ) , x ? S ( X ) } , where ? ( x ) = sup ? { ? x + y ? 2 + ? x ? y ? 2 , y ? S ( X ) } and ? ( x ) = inf ? { ? x + y ? 2 + ? x ? y ? 2 , y ? S ( X ) } are introduced and studied. The values of these parameters in the l p spaces and function spaces L p [ 0 , 1 ] are estimated. Among the other results, we proved that a Banachspace X with E ( X ) < 8 , or 2$"> f ( X ) > 2 is uniform nonsquare; and a Banachspace X with E ( X ) < 5 , or frac{32}{9}$"> f ( X ) > 32 / 9 has uniform normal structure.

We give a new proof of a recent characterization by Diaz and Mayoral of compactness in the Lebesgue-Bochner spaces $L_X^p$, where $X$ is a Banachspace and $1\\le p<\\infty$, and extend the result to vector-valued Banach function spaces $E_X$, where $E$ is a Banach function space with order continuous norm.

We prove that weakly unconditionally Cauchy (w.u.C.) series and unconditionally converging (u.c.) series are preserved under the action of polynomials or holomorphic functions on Banachspaces, with natural restrictions in the latter case. Thus it is natural to introduce the unconditionally converging polynomials, defined as polynomials taking w.u.C. series into u.c.\\ series, and analogously, the unconditionally converging holomorphic functions. We show that most of the classes of polynomials which have been considered in the literature consist of unconditionally converging polynomials. Then we study several ``polynomial properties'' of Banachspaces, defined in terms of relations of inclusion between classes of polynomials, and also some ``holomorphic properties''. We find remarkable differences with the corresponding ``linear properties''. For example, we show that a Banachspace $E$ has the polynomial property (V) if and only if the spaces of homogeneous scalar polynomials ${\\cal P}(^k\\!E)$, $k\\in{\\bf N}$,...

González, M; Gonzalez, Manuel; Gutierrez, Joaquin M.

We prove that weakly unconditionally Cauchy (w.u.C.) series and unconditionally converging (u.c.) series are preserved under the action of polynomials or holomorphic functions on Banachspaces, with natural restrictions in the latter case. Thus it is natural to introduce the unconditionally converging polynomials, defined as polynomials taking w.u.C. series into u.c.\\ series, and analogously, the unconditionally converging holomorphic functions. We show that most of the classes of polynomials which have been considered in the literature consist of unconditionally converging polynomials. Then we study several ``polynomial properties'' of Banachspaces, defined in terms of relations of inclusion between classes of polynomials, and also some ``holomorphic properties''. We find remarkable differences with the corresponding ``linear properties''. For example, we show that a Banachspace $E$ has the polynomial property (V) if and only if the spaces of homogeneous scalar polynomials ${\\cal P}(^k\\!E)$, $k\\in{\\bf N}$,...

We prove that if [tau] is a strongly continuous representation of a compact group G on a Banachspace X, then the weakly closed Banach algebra generated by the Fourier transforms with [mu][set membership, variant]M(G) is a semisimple Banach algebra.

This paper considers the problem of extending multilinear forms on a Banachspace X to a larger space Y containing it as a closed subspace. For instance, if X is a subspace of Y and X0 ! Y 0 extends linear forms, then the induced Nicodemi operators extend multilinear forms. It is shown that an exten...

Villanueva Díez, Ignacio; Cabello Sánchez, Félix; Garcia, R.

The aim of this paper is to emphasize various concepts of dichotomies for evolution equations in Banachspaces, due to the important role they play in the approach of stable, instable and central manifolds. The asymptotic properties of the solutions of the evolution equations are studied by means of...

We investigate a method of accelerated Landweber type for the iterative regularization of nonlinear ill-posed operator equations in Banachspaces. Based on an auxiliary algorithm with a simplified choice of the step-size parameter we present a convergence and stability analysis of the algorithm under consideration. We will close our discussion with the presentation of a numerical example.

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

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

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

the main goal of this paper is to prove that any Banachspace X, that every dual ball in X** is weak* -separable, or every weak* -closed convex subset in X** is weak* -separable, or every norm-closed convex set in X* is constructible, admits an equivalent Frechet differentiable norm.

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

Full Text Available We define a viscosity method for continuous pseudocontractive mappings defined on closed and convex subsets of reflexiveBanachspaces with a uniformly GÃƒÂ¢teaux differentiable norm. We prove the convergence of these schemes improving the main theorems in the work by Y. Yao et al. (2007) and H. Zhou (2008).

Filomena Cianciaruso; Giuseppe Marino; Luigi Muglia; Haiyun Zhou

Full Text Available We define a viscosity method for continuous pseudocontractive mappings defined on closed and convex subsets of reflexiveBanachspaces with a uniformly Gâteaux differentiable norm. We prove the convergence of these schemes improving the main theorems in the work by Y. Yao et al. (2007) and H. Zhou (2008).

Filomena Cianciaruso; Giuseppe Marino; Luigi Muglia; Haiyun Zhou

The class of countably intersected families of sets is defined. For any such family we define a Banachspace not containing $\\ell^{1}(\\NN )$. Thus we obtain counterexamples to certain questions related to the heredity problem for W.C.G. Banachspaces. Among them we give a subspace of a W.C.G. Banachspace not containing $\\ell^{1}(\\NN )$ and not being itself a W.C.G. space.

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

Introduction.Here, we study structures from functional analysis from the perspective of modeltheory. Specifically, we study structures that are based on Banachspaces, e.g.,Banach algebras, Banach lattices, Hilbert spaces with operators and, of course,Banachspaces themselves. Below, we refer to these structures as "analytic" structures,in order to distinguish them from "algebraic" structures, the structures thatare traditionally studied in model theory.Ever since the introduction of the ultrapower construction in analysis by D. DacunhaCastelleand J.-L. Krivine in [5] (see also [1]), the use of ideas and methods fromlogic in Banachspace theory has proved to be quite fruitful. Some of the deepestresults of Banachspace theory (e.g., Krivine's block finite representability theorem[20]) were proved using ideas from model theory. Numerous concepts andmethods that are now widely used in functional analysis were originally motivatedby analogies with logic. In some ca

Introduction.Here, we study structures from functional analysis from the perspective of modeltheory. Specifically, we study structures that are based on Banachspaces, e.g.,Banach algebras, Banach lattices, Hilbert spaces with operators and, of course,Banachspaces themselves. Below, we refer to these structures as "analytic" structures,in order to distinguish them from "algebraic" structures, the structures thatare traditionally studied in model theory.Ever since the introduction of the ultrapower construction in analysis by D. DacunhaCastelleand J.-L. Krivine in [5] (see also [1]), the use of ideas and methods fromlogic in Banachspace theory has proved to be quite fruitful. Some of the deepestresults of Banachspace theory (e.g., Krivine's block finite representability theorem[20]) were proved using ideas from model theory. Numerous concepts andmethods that are now widely used in functional analysis were originally motivatedby analogies with logic. In some case

We obtain the following characterization of Hilbert spaces. Let $E$ be a Banachspace whose unit sphere $S$ has a hyperplane of symmetry. Then $E$ is a Hilbert space iff any of the following two conditions is fulfilled: a) the isometry group ${\\rm Iso}\\, E$ of $E$ has a dense orbit in S; b) the identity component $G_0$ of the group ${\\rm Iso}\\, E$ endowed with the strong operator topology acts topologically irreducible on $E$. Some related results on infinite dimentional Coxeter groups generated by isometric reflexions are given which allow to analyse the structure of isometry groups containing sufficiently many reflexions.

We develop a theory of Malliavin calculus for Banachspace valued random variables. Using radonifying operators instead of symmetric tensor products we extend the Wiener-Ito isometry to Banachspaces. In the white noise case we obtain two sided L^p-estimates for multiple stochastic integrals in arbitrary Banachspaces. It is shown that the Malliavin derivative is bounded on vector-valued Wiener-Ito chaoses. Our main tools are decoupling inequalities for vector-valued random variables. In the opposite direction we use Meyer's inequalities to give a new proof of a decoupling result for Gaussian chaoses in UMD Banachspaces.

Full Text Available In this paper we consider the questions of existence and uniqueness of solutions of certain semilinear and quasilinear evolution equations on Banachspace. 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. Further, quasilinear stochastic evolution equations seemingly have never been considered in the literature.

Pruitt's estimates on the expectation and the distribution of the time taken by a random walk to exit a ball of radius r are extended to the infinite dimensional setting. It is shown that they separate into two pairs of estimates depending on whether the space is type 2 or cotype 2. It is further shown that these estimates characterize type 2 and cotype 2 spaces.

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

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

Full Text Available The convex feasibility problem (CFP) of finding a point in the nonempty intersection is considered, where is an integer and each is assumed to be the fixed point set of a nonexpansive mapping , where is a reflexiveBanachspace 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 , where is a nonempty closed convex subset of and for any given the iterative scheme is strongly convergent to a solution of (CFP), if and only if and satisfy certain conditions, where and is a sunny nonexpansive retraction of onto . 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).

Chang Shih-Sen; Yao Jen-Chih; Kim Jong Kyu; Yang Li

Full Text Available We give sufficient conditions that allow contractible (resp., reflexive amenable) Banach algebras to be finite-dimensional and semisimple algebras. Moreover, we show that any contractible (resp., reflexive amenable) Banach algebra in which every maximal left ideal has a Banachspace complement is indeed a direct sum of finitely many full matrix algebras. Finally, we characterize Hermitian *-algebras that are contractible.

We give sufficient conditions that allow contractible (resp., reflexive amenable) Banach algebras to be finite-dimensional and semisimple algebras. Moreover, we show that any contractible (resp., reflexive amenable) Banach algebra in which every maximal left ideal has a Banachspace complement is in...

The aim of this paper is to extend the framework of the spectral method for proving property (T) to the class of reflexiveBanachspaces and present conditions implying that every affine isometric action of a given group $G$ on a reflexiveBanachspace $X$ has a fixed point. This last property is a strong version of Kazhdan's property (T) and is equivalent to the fact that $H^1(G,\\pi)=0$ for every isometric representation $\\pi$ of $G$ on $X$. We give examples of groups for which every affine isometric action on an $L_p$ space has a fixed point for certain $p>2$, and present several applications. In particular, we give a lower bound on the conformal dimension of the boundary of a hyperbolic group in the Gromov density model.

Cylindrical probability measures are finitely additive measures on Banachspaces that have sigma-additive projections to Euclidean spaces of all dimensions. They are naturally associated to notions of weak (cylindrical) random variable and hence weak (cylindrical) stochastic processes. In this paper we focus on cylindrical Levy processes. These have (weak) Levy-Ito decompositions and an associated Levy-Khintchine formula. If the process is weakly square integrable, its covariance operator can be used to construct a reproducing kernel Hilbert space in which the process has a decomposition as an infinite series built from a sequence of uncorrelated bona fide one-dimensional Levy processes. This series is used to define cylindrical stochastic integrals from which cylindrical Ornstein-Uhlenbeck processes may be constructed as unique solutions of the associated Cauchy problem. We demonstrate that such processes are cylindrical Markov processes and study their (cylindrical) invariant measures.

Given 0 < s ? 1 and ? an s-convex function, s - ? -sequence spaces are introduced. Several quasi-Banach sequence spaces are thus characterized as a particular case of s - ? -spaces. For these spaces, new measures of noncompactness are also defined, related to the Hausdorff measure of noncompactness. As an application, compact sets in s - ? -interpolation spaces of a quasi-Banach couple are studied.

This paper is concerned with the characterization of $\\alpha$-modulation spaces by Banach frames, i.e., stable and redundant non-orthogonal expansions, constituted of functions obtained by a suitable combination of translation, modulation and dilation of a mother atom. In particular, the parameter $\\alpha \\in [0,1]$ governs the dependence of the dilation factor on the frequency. The result is achieved by exploiting intrinsic properties of localization of such frames. The well-known Gabor and wavelet frames arise as special cases ($\\alpha = 0$) and limiting case ($ \\alpha \\to 1)$, to characterize respectively modulation and Besov spaces. This intermediate theory contributes to a further answer to the theoretical need of a common interpretation and framework between Gabor and wavelet theory and to the construction of new tools for applications in time-frequency analysis, signal processing, and numerical analysis.

We prove in this article that every Borelian measure, for example, the distribution of a random variable, in separable Banachspace has a support which is compact embedded Banach subspace; and prove that if the norm of the random variable belongs to some exponential Orlicz space, then the new subspace can be choose such that the norm of this variable in the new space also belongs to other exponential Orlicz space.

A dual Banach algebra is a Banach algebra which is a dual space, with the multiplication being separately weak$^*$-continuous. We show that given a unital dual Banach algebra $\\mc A$, we can find a reflexiveBanachspace $E$, and an isometric, weak$^*$-weak$^*$-continuous homomorphism $\\pi:\\mc A\\to\\mc B(E)$ such that $\\pi(\\mc A)$ equals its own bicommutant.

We introduce and study the following modified version of the Invariant Subspace Problem: whether every operator T on a Banachspace has an almost invariant half-space, that is, a subspace Y of infinite dimension and infinite codimension such that Y is of finite codimension in T(Y). We solve this problem in the affirmative for a large class of operators which includes quasinilpotent weighted shift operators on l_p (1 \\le p < \\infty) or c_0.

Androulakis, George; Tcaciuc, Adi; Troitsky, Vladimir G

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

We prove that there exist Banachspaces 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 Banachspaces with PCP." J. Funct. Anal. 253 (2007) 772-781.

Reflexive cones in Banachspaces are cones with weakly compact intersection with the unit ball. In this paper we study the structure of this class of cones. We investigate the relations between the notion of reflexive cones and the properties of their bases. This allows us to prove a characterization of reflexive cones in term of the absence of a subcone isomorphic to the positive cone of \\ell_{1}. Moreover, the properties of some specific classes of reflexive cones are investigated. Namely, we consider the reflexive cones such that the intersection with the unit ball is norm compact, those generated by a Schauder basis and the reflexive cones regarded as ordering cones in a Banachspaces. Finally, it is worth to point out that a characterization of reflexivespaces and also of the Schur spaces by the properties of reflexive cones is given.

Casini, Emanuele; Polyrakis, Ioannis A; Xanthos, Foivos

Full Text Available We introduce and study Clarkson, Dol’nikov-Pichugov, Jacobi and mutual diameter constants reflecting the geometry of a Banachspace and Clarkson, Jacobi and Pichugov classes of Banachspaces and their relations with James, self-Jung, Kottman and Schäffer constants in order to establish quantitative versions of Hahn-Banach separability theorem and to characterise the isometric extendability of Hölder-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.

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

Let $X$ be a complex Banachspace 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 strictly convex complex Banachspace.

Tensor-based methods are receiving a growing interest in scientific computing for the numerical solution of problems defined in high dimensional tensor product spaces. A family of methods called Proper Generalized Decompositions methods have been recently introduced for the a priori construction of tensor approximations of the solution of such problems. In this paper, we give a mathematical analysis of a family of progressive and updated Proper Generalized Decompositions for a particular class of problems associated with the minimization of a convex functional over a reflexive tensor Banachspace.

Let X be a Banachspace. Given a subset A of the dual space X* denote by $A_{(1)}$ the weak* sequential closure of A, i.e., the set of all limits of weak*-convergent sequences in A. The study of weak* sequential closures of linear subspaces of the duals of separable Banachspaces was initiated by S.Banach. The first results of this study were presented in the appendix to his book "Theorie des operations lineaires" (1932). It is natural to suppose that the reason for studying weak* sequential closures by S. Banach and S. Mazurkiewicz was the lack of acquaintance of S. Banach and his school with concepts of general topology. Although the name "General topology" was introduced later, the subject did already existed. F. Hausdorff introduced topological spaces in his book published in 1914, Alexandroff-Urysohn (1924) studied compactness, and A.Tychonoff published his theorem on compactness of products in 1929. Also J.von Neumann introduced the notion of a weak topology in his paper published in 1929. Using the not...

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

The present paper considers two concepts of nonuniform exponential dichotomy (in the sense of Barreira-Valls) for evolution operators in Banachspaces. Some examples clarify the relations between these concepts. A variant for the case of nonuniform exponential dichotomy of a well-known theorem due to Datko is obtained. We also prove a sufficient condition for the existence of exponential dichotomy of evolution operators in terms of the existence of a Lyapunov function in the general case of Banachspaces. We emphasize that in our proof we do not need to assume that the evolution operator is invertible on the unstable subspace.

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

The aim of this paper is to give several characterizations for the property of weak exponential expansiveness for evolution families in Banachspaces. Variants for weak exponential expansiveness of some well-known results in stability theory (Datko (1973), Rolewicz (1986), Ichikawa (1984), and Megan et al. (2003)) are obtained.

This paper emphasizes a couple of characterizations for the exponential instability property of skew-evolution semiflows in Banachspaces, defined by means of evolution semiflows and evolution cocycles. Some Datko type results for this asymptotic behavior are proved. There is provided a unified trea...

The paper emphasizes some asymptotic behaviors for skew-evolution semiflows in Banachspaces. These are defined by means of evolution semiflows and evolution cocycles. Some characterizations which generalize classical results are also provided. The approach is from nonuniform point of view.

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 Banachspace l2 and Lp[0,1]? ?(1

Full Text Available We consider optimization problems in Banachspaces, whose cost functions are convex and smooth, but do not possess strengthened convexity properties. We propose a general class of iterative methods, which are based on combining descent and regularization approaches and provide strong convergence of iteration sequences to a solution of the initial problem.

Let $X$ be a Banachspace with a separable dual $X^{*}$. Let $Y\\subset X$ be a closed subspace, and $f:Y\\to\\mathbb{R}$ a $C^{1}$-smooth function. Then we show there is a $C^{1}$ extension of $f$ to $X$.

The paper considers three concepts of polynomial stability for linear evolution operators which are defined in a general Banachspace and whose norms can increase not faster than exponentially. Our approach is based on the extension of techniques for exponential stability to the case of polynomial ...

Mihail Megan; Traian Ceau?u; Magda Lumini?a Ramnean?u

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

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

Let x be a real Banachspace and C a subset of x. We consider a non expansive map t from an arbitrary subset C of x into itself, and for x is an element of C, we study the asymptotic behaviour of the sequence xTxn in x. 20 refs.

The Lagrange interpolation problem in Banachspaces is approached by cardinal basis interpolation. Some error estimates are given and the results of several numerical tests are reported in order to show the approximation performances of the proposed interpolants. A comparison between some examples o...

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

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

Full Text Available Let ÃÂ€:EÃ¢Â†Â’X and ÃÂ:FÃ¢Â†Â’X be bundles of Banachspaces, where X is a compact Hausdorff space, and let V be a Banachspace. Let ÃŽÂ“(ÃÂ€) denote the space of sections of the bundle ÃÂ€. We obtain two representations of integral operators T:ÃŽÂ“(ÃÂ€)Ã¢Â†Â’V in terms of measures. The first generalizes a recent result of P. Saab, the second generalizes a theorem of Grothendieck. We also study integral operators T:ÃŽÂ“(ÃÂ€)Ã¢Â†Â’ÃŽÂ“(ÃÂ) which are C(X)-linear.

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 Banachspaces, 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...

Let H be a separable real Hilbert space and let F = (F_t)_{t\\in [0,T]} be the augmented filtration generated by an H-cylindrical Brownian motion W_H on [0,T]. We prove that if E is a UMD Banachspace, 1\\leq p<\\infty, and f\\in D^{1,p}(E) is F_T-measurable, then f = \\E f + \\int_0^T P_F(Df) dW_H where D is the Malliavin derivative and P_F is the projection onto the F-adapted elements in a suitable Banachspace of L^p-stochastically integrable L(H,E)-valued processes.

In this paper, we prove that the Banach contraction principle proved by S. G. Matthews in 1994 on 0--complete partial metric spaces can be extended to cyclical mappings. However, the generalized contraction principle proved by D. Ili\\'{c}, V. Pavlovi\\'{c} and V. Rako\\u{c}evi\\'{c} in "Some new extensions of Banach's contraction principle to partial metric spaces, Appl. Math. Lett. 24 (2011), 1326--1330" on complete partial metric spaces can not be extended to cyclical mappings. Some examples are given to illustrate the effectiveness of our results. Moreover, we generalize some of the results obtained by W. A. Kirk, P. S. Srinivasan and P. Veeramani in "Fixed points for mappings satisfying cyclical contractive conditions, Fixed Point Theory 4 (1) (2003),79--89". Finally, an Edelstein's type theorem is also extended in case one of the sets in the cyclic decomposition is 0-compact.

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 Banachspaces, 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.

Full Text Available In this paper we study a second order semilinear initial value problem (IVP), where the linear operator in the differential equation is the infinitesimal generator of a strongly continuous cosine family in a Banachspace E. We shall first prove existence, uniqueness and estimation results for weak solutions of the IVP with Carathéodory type of nonlinearity, by using a comparison method. The existence of the extremal mild solutions of the IVP is then studied when E is an ordered Banachspace. We shall also discuss the dependence of these solutions on the data. A characteristic feature of the results concerning extremal solutions is that the nonlinearity is not assumed to be continuous in any of its arguments. Moreover, no compactness conditions are assumed. The obtained results are then applied to a second order partial differential equation of hyperbolic type.

Full Text Available We show the existence and uniqueness of classical solutions of the nonautonomous second-order equation: uÃ¢Â€Â³(t)=A(t)uÃ¢Â€Â²(t)+B(t)u(t)+f(t), 0Ã¢Â‰Â¤tÃ¢Â‰Â¤T; u(0)=x0, uÃ¢Â€Â²(0)=x1 on a Banachspace by means of operator matrix method and apply to Volterra integrodifferential equations.

Evolutionary equations are studied in abstract Banachspaces 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

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

Multipliers have been recently introduced as operators for Bessel sequences and frames in Hilbert spaces. These operators are defined by a fixed multiplication pattern (the symbol) which is inserted between the analysis and synthesis operators. In this paper, we will generalize the concept of Bessel multipliers for p-Bessel and p-Riesz sequences in Banachspaces. It will be shown that bounded symbols lead to bounded operators. Symbols converging to zero induce compact operators. Furthermore, we will give sufficient conditions for multipliers to be nuclear operators. Finally, we will show the continuous dependency of the multipliers on their parameters.

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

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

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

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 .

We prove that for every infinite-dimensional Banachspace 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 Banachspace Y having a (not necessarily equivalent) C-p norm (with p is an element of N boole...

Full Text Available In 1965, Kirk proved that if is a nonempty weakly compact convex subset of a Banachspace with normal structure, then every nonexpansive mapping has a fixed point. The purpose of this paper is to outline various generalizations of Kirk's fixed point theorem to semigroup of nonexpansive mappings and for Banachspaces associated to a locally compact group.

We prove the following new characterization of $C^p$ (Lipschitz) smoothnessin Banachspaces. An infinite-dimensional Banachspace $X$ has a $C^p$ smooth(Lipschitz) bump function if and only if it has another $C^p$ smooth(Lipschitz) bump function $f$ such that $f'(x)\

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

The paper introduces the notion of skew-evolution semiflows and presents the concept of pointwise trichotomy in the case of skew-evolution semiflows on a Banachspace. The connection with the classic notion of trichotomy presented by us in a previous paper in 2006 for evolution operators, is also emphasized, as well as some characterizations. The approach of the theory is from uniform point of view. The study can also be extended to systems with control whose state evolution can be described by skew-evolution semiflows.

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 Banachspaces. 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.

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

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

Let $X$ be a separable Banachspace with a separating polynomial. We show that there exists $C\\geq 1$ such that for every Lipschitz function $f:X\\rightarrow\\mathbb{R}$, and every $\\varepsilon>0$, there exists a Lipschitz, real analytic function $g:X\\rightarrow\\mathbb{R}$ such that $|f(x)-g(x)|\\leq \\varepsilon$ and $\\textrm{Lip}(g)\\leq C\\textrm{Lip}(f)$. This result is new even in the case when $X$ is a Hilbert space. Furthermore we characterize the class of Banachspaces having this approximation property as those Banachspaces $X$ having a Lipschitz, real-analytic separating function (meaning a Lipschitz, real analytic function $Q:X\\to [0, +\\infty)$ such that $Q(0)=0$ and $Q(x)\\geq \\|x\\|$ for $\\|x\\|\\geq 1$).

Let $X$ and $Y$ be separable Banachspaces and denote by $\\sss\\sss(X,Y)$ the subset of $\\llll(X,Y)$ consisting of all strictly singular operators. We study various ordinal ranks on the set $\\sss\\sss(X,Y)$. Our main results are summarized as follows. Firstly, we define a new rank $\\rs$ on $\\sss\\sss(X,Y)$. We show that $\\rs$ is a co-analytic rank and that dominates the rank $\\varrho$ introduced by Androulakis, Dodos, Sirotkin and Troitsky [Israel J. Math., 169 (2009), 221-250]. Secondly, for every $1\\leq p<+\\infty$ we construct a Banachspace $Y_p$ with an unconditional basis such that $\\sss\\sss(\\ell_p, Y_p)$ is a co-analytic non-Borel subset of $\\llll(\\ell_p,Y_p)$ yet every strictly singular operator $T:\\ell_p\\to Y_p$ satisfies $\\varrho(T)\\leq 2$. This answers a question of Argyros.

Full Text Available The existence of mild solutions of Sobolev-type semilinear mixed integrodifferential inclusions in Banachspaces is proved using a fixed point theorem for multivalued maps on locally convex topological spaces.

We find necessary and sufficient conditions for a Banachspace operator T to satisfy the generalized Browder's theorem, and we obtain new necessary and sufficient conditions to guarantee that the spectral mapping theorem holds for the B-Weyl spectrum and for polynomials in T. We also prove that the spectral mapping theorem holds for the B-Browder spectrum and for analytic functions on an open neighborhood of \\sigma(T). As applications, we show that if T is algebraically M-hyponormal, or if T is algebraically paranormal, then the generalized Weyl's theorem holds for f(T), where f \\in H(T), the space of functions analytic on an open neighborhood of \\sigma(T). We also show that if T is reduced by each of its eigenspaces, then the generalized Browder's theorem holds for f(T), for each f \\in H(\\sigma(T)).

Full Text Available Let $B(X)$ denote the family of all nonempty closed bounded subsets of a real Banachspace $X$, endowed with the Hausdorff metric. For $E, F \\in B(X)$ we set $\\lambda _{EF} = inf \\{\\|z - x\\| : x \\in E, z \\in F \\}$. Let $D$ denote the closure (under the maximum distance) of the set of all $(E, F) \\in B(X) \\times B(X)$ such that $\\lambda {EF} > 0$. It is proved that the set of all $(E, F) \\in 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 $D$.

This is the second part in a series dealing with subspaces of de Branges spaces of entire function generated by majorization on subsets of the closed upper half-plane. In this part we investigate certain Banachspaces generated by admissible majorants. We study their interplay with the original de Branges space structure, and their geometry. In particular, we will show that, generically, they will be nonreflexive and nonseparable.

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

Kretov M.; Malakhovsky V.; Semenov V.; Khudenko V.

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 Banachspace setting. Numerical experiments illustrate the performance of the method.

We established some theorems under the aim of deriving variants of the Banach contraction principle, using the classes of inner contractions and outer contractions, on the structure of fuzzy modular spaces.

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

Characterization of the mapping properties such as boundedness, compactness, measure of non-compactness and estimates of the approximation numbers of Hardy-type integral operators in Banach function spaces are given.

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

Full Text Available Operator self-similar (OSS) stochastic processes on arbitrary Banachspaces are considered. If the family of expectations of such a process is a spanning subset of the space, it is proved that the scaling family of operators of the process under consideration is a uniquely determined multiplicative group of operators. If the expectation-function of the process is continuous, it is proved that the expectations of the process have power-growth with exponent greater than or equal to 0, that is, their norm is less than a nonnegative constant times such a power-function, provided that the linear space spanned by the expectations has category 2 (in the sense of Baire) in its closure. It is shown that OSS processes whose expectation-function is differentiable on an interval (s0,Ã¢ÂˆÂž), for some s0Ã¢Â‰Â¥1, have a unique scaling family of operators of the form {sH:s>0}, if the expectations of the process span a dense linear subspace of category 2. The existence of a scaling family of the form {sH:s>0} is proved for proper Hilbert space OSS processes with an Abelian scaling family of positive operators.

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

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

Wiener spaces and B-valued Wiener processes. An abstractWiener space [14], [17] is by definition a triple (B; H;) which consists of aseparable Banachspace B with norm j Delta j B , a separable Hilbert space H which isa vector subspace of B with the canonical embedding i : H ,! B, and a Gaussianmeasure on the Borel oe -field B of B with covariance H. For simplicity, we onlyconsider throughout this work centered Gaussian measures. Thus is the uniqueprobability measure on (B; B) such that each continuous linear functional on8 M. LEDOUX, T. LYONS, Z. QIANB has normal distribution N (0; jj2H ). For any 2 B,! H, define the pairingj : B ! R between Band B by j (x) = hx; i. Then B is the smallest oe-fieldsuch that all functions j are measurable and is the unique probability measureon (B; B) such thatZBexp(ihx; i)(dx) = exp`Gamma12jj2H'for any 2 B. The coordinate function e(x) = x is a B-valued Gaussian randomvariable under the probability .

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 Banachspace. 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 Banachspaces. J. Math. Anal. Appl. 341 (2008) 1–11]. The results generalize the corresponding results.

Full Text Available Based on the notion of -accretive mappings and the resolvent operators associated with -accretive mappings due to Lan et al., we study a new class of multivalued nonlinear variational inclusion problems with -accretive mappings in Banachspaces and construct some new iterative algorithms to approximate the solutions of the nonlinear variational inclusion problems involving -accretive mappings. We also prove the existence of solutions and the convergence of the sequences generated by the algorithms in -uniformly smooth Banachspaces.

Full Text Available In 1965, Kirk proved that if C is a nonempty weakly compact convex subset of a Banachspace with normal structure, then every nonexpansive mapping T:C?C has a fixed point. The purpose of this paper is to outline various generalizations of Kirk's fixed point theorem to semigroup of nonexpansive mappings and for Banachspaces associated to a locally compact group.

We introduce UDSp-property (resp. UDTq-property) in Banach lattices as the property that every normalized disjoint sequence has a subsequence with an upper p-estimate (resp. lower q-estimate). In the case of rearrangement invariant spaces, the relationships with Boyd indices of the space are studied. Some applications of these properties are given to the high order smoothness of Banach lattices, in the sense of the existence of differentiable bump functions.

We study Banach-valued holomorphic functions defined on open subsets of the maximal ideal space of the Banach algebra H^\\infty of bounded holomorphic functions on the unit disk D\\subset C with pointwise multiplication and supremum norm. In particular, we establish vanishing cohomology for sheaves of germs of such functions and, solving a Banach-valued corona problem for H^\\infty, prove that the maximal ideal space of the algebra H_{\\rm comp}^\\infty (A) of holomorphic functions on $\\Di$ with relatively compact images in a commutative unital complex Banach algebra A is homeomorphic to the direct product of maximal ideal spaces of H^\\infty and A.

The notion of diameter D of the state space of a Jordan Banach algebra (JBW-algebra A) is introduced. The diameters of the state spaces for JBW-factors of type \\mathrm{I}_n ( n<+\\infty), \\mathrm{I}_\\infty, \\mathrm{II}_1, \\mathrm{II}_\\infty, \\mathrm{III}_\\lambda, ( 0<\\lambda<1) are computed. It is proved that if A is not a factor, or is a factor of type \\mathrm{I}_\\infty or \\mathrm{II}_1, then D(A)=2. If A is a JBW-factor of type \\mathrm{I}_n ( n<+\\infty), then D(A)=2(1-1/n), and if A is a JBW-factor of type \\mathrm{III}_\\lambda, ( 0<\\lambda<1), then D(A)=2(1-\\sqrt\\lambda)(1+\\sqrt\\lambda) or D(A)=2(1-\\root4\\of\\lambda)(1+\\root4\\of\\lambda). Bibliography: 15 titles.

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

Full Text Available Abstract in spanish Estudiamos el espectro de los multiplicadores (operadores acotados que conmutan con el operador shift ) en un espacio de Banach de sucesiones en (more) 1041" src="http://fbpe/img/cubo/v14n3/art02-04.jpg" alt="http://fbpe/img/cubo/v14n3/art02-04.jpg">. Dado un multiplicador , probamos que donde es el símbolo de . Obtenemos un resultados similar para el espectro de un operador que conmuta con el shift en un espacio de Banach de sucesiones en . Generalizamos los resultados sobre multiplicadores en espacios de Banach de sucesiones en . Abstract in english We study the spectrum of multipliers (bounded operators commuting with the shift operator ) on a Banachspace of sequences on (more) bpe/img/cubo/v14n3/art02-04.jpg" alt="http://fbpe/img/cubo/v14n3/art02-04.jpg">. Given a multiplier , we prove that where is the symbol of . We obtain a similar result for the spectrum of an operator commuting with the shift on a Banachspace of sequences on . We generalize the results for multipliers on Banachspaces of sequences on .

In this paper we show the weak Banach-Saks property of the Banach vector space $(L_\\mu^p)^m$ generated by $m$ $L_\\mu^p$-spaces for $1\\leq p<+\\infty,$ where $m$ is any given natural number. When $m=1,$ this is the famous Banach-Saks-Szlenk theorem. By use of this property, we also present inequalities for integrals of functions that are the composition of nonnegative continuous convex functions on a convex set of a vector space ${\\bf R}^m$ and vector-valued functions in a weakly compact subset of the space $(L_\\mu^p)^m$ for $1\\leq p<+\\infty$ and inequalities when these vector-valued functions are in a weakly* compact subset of the product space $(L_\\mu^\\infty)^m$ generated by $m$ $L_\\mu^\\infty$-spaces.

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.

Full Text Available We give necessary and sufficient conditions for the periodicity of mild solutions to the the higher order differential equation $u^{(n)}(t)=Au(t)+f(t)$, $0le t le T$, in a Banachspace $E$. Applications are made to the cases, when $A$ generates a $C_0$-semigroup or a cosine family, and when $E$ is a Hilbert space.

We introduce UDSp-property (resp. UDTq-property) in Banach lattices as the property that every normalized disjoint sequence has a subsequence with an upper p-estimate (resp. lower q-estimate). In the case of rearrangement invariant spaces, the relationships with Boyd indices of the space are studied...

Full Text Available In the present paper we prove a sufficient condition and a characterization for the stability of linear skew-product semiflows by using Lyapunov function, in Banachspaces. These are generalizations of the results obtained in Ahmed N. U., Semigroups Theory with Applications to Systems and Control, Pittman Research, Notes Math., 1991. and Preda C. and Preda P., Lyapunov operator inequalities for exponential stability of Banachspace semigroups of operators, Appl. Math. Letters 25(3) (2012), 401-403. for the case of C0-semigroups. Moreover, there are presented the discrete variants of the results mentioned above.

{\\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.

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

Inverse problems can usually be modelled as operator equations in infinite-dimensional spaces with a forward operator acting between Hilbert or Banachspaces—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 Banachspace 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 Banachspaces, 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 Banachspaces. 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 Banachspaces 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 Banachspaces, 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 Banachspace to general operators in place of the inverse duality mapping, which corresponds to the use of general regularization functionals in variational regularization. The L? topology in data space corresponds to the frequently occuring situation of uniformly distributed data noise. A numerically efficient solution of the resulting Tikhonov regularization problem via a Moreau-Yosida appriximation and a semismooth Newton method, along with a ?-free regularization parameter choice rule, is the topic of the paper L? fitting for inverse problems with uniform noise by Christian Clason. Extension of convergence rates results from classical source conditions to their generalization via variational inequalities with a priori and a posteriori stopping rules is the main contribution of the paper Regularization of linear ill-posed problems by the augmented Lagrangian method and variational inequalities by Klaus Frick and Markus Grasmair, again in the context of some iterative method. A powerful tool for proving convergence rates of Tikhonov type but also othe

Schuster, Thomas; Hofmann, Bernd; Kaltenbacher, Barbara

We establish triviality of some holomorphic Banach vector bundles on the maximal ideal space of the Banach algebra of bounded holomorphic functions on the unit disk with pointwise multiplication and supremum norm. We apply the result to the study of the Sz.-Nagy operator corona problem.

Let $(M,\\Gamma)$ be a Hopf--von Neumann algebra, so that $M_\\ast$ is a completely contractive Banach algebra. We investigate whether the product of two elements of $M$ that are both weakly almost periodic functionals on $M_\\ast$ is again weakly almost periodic. For that purpose, we establish the following factorization result: If $M$ and $N$ are injective von Neumann algebras, and if $x, y \\in M \\bar{\\otimes} N$ correspond to weakly compact operators from $M_\\ast$ to $N$ factoring through reflexive operator spaces $X$ and $Y$, respectively, then the operator corresponding to $xy$ factors through the Haagerup tensor product $X \\otimes^h Y$ provided that $X \\otimes^h Y$ is reflexive. As a consequence, for instance, for any Hopf--von Neumann algebra $(M,\\Gamma)$ with $M$ injective, the product of a weakly almost periodic element of $M$ with a completely almost periodic one is again weakly almost periodic.

We show that if a Banachspace 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.

While the topological and geometrical properties of convex bodies in Banachspaces are quite well understood (including their topological and smooth classification), much less is known about the structure of starlike bodies. Starlike bodies are important objects in nonlinear functional analysis as t...

Azagra Rueda, Daniel; Jiménez Sevilla, María del Mar

We consider a nonlinear Volterra integral inclusion in a Banachspace. We establish the existence of extremal integral solutions, and we show that they are dense in the solution set of the original equation. As an important application, we obtain a ?bang-bang? theorem for a class of nonlin...

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

The paper emphasizes the property of stability for skew-evolution semiflows on Banachspaces, defined by means of evolution semiflows and evolution cocycles and which generalize the concept introduced by us in a previous paper. There are presented several general characterizations of this asymptotic...

The paper emphasizes the properties of exponential dichotomy and exponential trichotomy for skew-evolution semiflows in Banachspaces, by means of evolution semiflows and evolution cocycles. The approach is from uniform point of view. Some characterizations which generalize classic results are also ...

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

This paper studies steady-state control and stability for a class of integrodifferential control system with pulse-width modulated sampler on Banachspaces. The existence and stability of the steady-state for the integrodifferential control system with pulse-width modulated sampler are given. An exa...

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

In this work, we establish a sufficient condition for the controllability of the first-order impulsive neutral functional differential inclusions with infinite delay in Banachspaces. The results are obtained by using the Dhage's fixed point theorem.

Chang, Y.-K. [Department of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070 (China)], E-mail: lzchangyk@163.com; Anguraj, A. [Department of Mathematics, PSG College of Arts and Science, Coimbatore 641 014, Tamil Nadu (India)], E-mail: angurajpsg@yahoo.com; Mallika Arjunan, M. [Department of Mathematics, PSG College of Arts and Science, Coimbatore 641 014, Tamil Nadu (India)], E-mail: arjunphd07@yahoo.co.in

The aim of this paper is to review the state-of-the-art of recent research concerning the numerical index of Banachspaces, by presenting some of the results found in the last years and proposing a number of related open problems.

Kadets, V; Paya, R; Kadets, Vladimir; Martin, Miguel; Paya, Rafael

Full Text Available We investigate the maximal and minimal solutions of initial value problem for N-th order nonlinear impulsive integro-differential equation in Banachspace by establishing a comparison result and using the upper and lower solutions methods.

We show that if Y is a separable subspace of a Banachspace X such that both X and the quotient X/Y have C-p-smooth Lipschitz bump functions, and U is a bounded open subset of X, then, for every uniformly continuous function f : Y boolean AND U --> R and every epsilon > 0, there exists a C-p-smooth ...

Azagra Rueda, Daniel; Fry, Robb; Montesinos Matilla, Luis Alejandro

Two well-known fixed point iteration methods are applied to approximate fixed points of quasi-contractive maps in real uniformly smooth Banachspaces. While our theorems generalize important known results, our method is of independent interest. (author). 25 refs

Full Text Available In this article we extend the concept psi-exponential and psi-ordinary dichotomies for homogeneous linear differential equations in a Banachspace. 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.

Full Text Available Let K be a complete non-archimedean valued field of any rank, and let E be a K-Banachspace with a countable topological base. We determine the algebraic dimension of E (2.3, 2.4, 3.1).

Full Text Available Abstract in english Let K be a complete non-archimedean valued field of any rank, and let E be a K-Banachspace with a countable topological base. We determine the algebraic dimension of E (2.3, 2.4, 3.1).

Under the assumption that the continuum c is a regular cardinal, we prove the existence and uniqueness of a Boolean algebra B of size c defined by sharing the main structural properties that P(N)/fin has under CH and in the aleph2-Cohen model. We prove a similar result in the category of Banachspaces.

Full Text Available In this paper we study two concepts of exponential stability for vari-ational nonautonomous dierence equations in Banachspaces. Char-acterizations of these concepts are given. The obtained results can beconsidered as generalizations for variational nonautonomous dierenceequations of some well-known theorems due to Barbashin and Datko .

Mihail Megan; Traian Ceausu; Mihaela Aurelia Tomescu

Full Text Available For the linear equation $x'= A(t)x$ with recurrent (almost periodic) coefficients in an arbitrary Banachspace, we prove that the asymptotic stability of the null solution and of all limit equations implies the uniform stability of the null solution.

Full Text Available In this paper, we study the stability of the spectra of bounded linear operators B(X) in a Banachspace X, and obtain that their spectra are stable on a dense residual subset of B(X).

We characterize the class of separable Banachspaces $X$ such that for every continuous function $f:X\\to\\mathbb{R}$ and for every continuous function $\\epsilon:X\\to\\mathbb(0,+\\infty)$ there exists a $C^1$ smooth function $g:X\\to\\mathbb{R}$ for which $|f(x)-g(x)|\\leq\\epsilon(x)$ and $g'(x)\

Full Text Available An abstract, nonlinear, differential equation in Banachspace 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.

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 Banachspaces. 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).

Full Text Available Let X be a uniformly convex Banachspace, and let S,Ã‚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.

Full Text Available We establish strong convergence theorem for multi-step iterative scheme with errors for asymptotically nonexpansive mappings in the intermediate sense in Banachspaces. Our results extend and improve the recent ones announced by Plubtieng and Wangkeeree (2006), and many others.

In the paper is considered two problems on extension of operators whose range space for the first problem (or domain space for the second one) belongs to the fixed class of finite equivalence, which is generated by a given Banachspace $X$. Both problems are considered in two variants: isometric and isomorphic ones. Received a full solution of the first problem and the solution, close to final one for the second problem.

In the paper is considered two problems on extension of operators whose range space for the first problem (or domain space for the second one) belongs to the fixed class of finite equivalence, which is generated by a given Banachspace $X$. Both problems are considered in two variants: isometric and isomorphic ones. Received a full solution of the first problem and the solution, close to final one for the second problem.

In the paper is considered two problems on extension of operators whose range space for the first problem (or domain space for the second one) belongs to the fixed class of finite equivalence, which is generated by a given Banachspace $X$. Both problems are considered in two variants: isometric and isomorphic ones. Received a full solution of the first problem and the solution, close to final one for the second problem.

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

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

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

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

We study (local) martingale problems on a general separable Banachspace E and apply our results to stochastic evolution equations. In particular, we prove that if such an equation is well-posed, then the solutions are strong Markov processes. We apply our results to semilinear stochastic partial differential equations with multiplicative noise. As state space E, we consider Lebesgue spaces L^p in the range p \\in [1, \\infty), Sobolev spaces or spaces of continuous functions. The noise is either space-time white noise or given by finitely many independent Brownian motions.

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 Banachspace. Then, we obtain a strong convergence theorem for the sequence generated by those process in Banachspaces. Moreover, we obtain new resultfor finding a zero point of maximal monotone operators in a Banachspace. 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 Banachspaces, Nonlinear Anal. 70 (2009) 45--57.] Qin, Cho and Kang [Convergence theorems of common elements forequilibrium problems and fixed point problems in Banachspaces, 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 Banachspaces, Fixed Point Theory Appl., (2009), Article ID 719360, 18 pages] and many authors.

Kriengsak Wattanawitoon; Usa Hamphries; Poom Kumam

By making use of duality mappings, we formulate an inexact Newton-Landweber iteration method for solving nonlinear inverse problems in Banachspaces. The method consists of two components: an outer Newton iteration and an inner scheme providing the increments by applying the Landweber iteration in Banachspaces 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.

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

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

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

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

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

Full Text Available We introduce and study the general nonlinear random -accretive equations with random fuzzy mappings. By using the resolvent technique for the -accretive operators, we prove the existence theorems and convergence theorems of the generalized random iterative algorithm for this nonlinear random equations with random fuzzy mappings in -uniformly smooth Banachspaces. Our result in this paper improves and generalizes some known corresponding results in the literature.

Full Text Available The purpose of this paper is to use the modified block iterative method to propose an algorithm for solving the convex feasibility problems for an infinite family of quasi-?-asymptotically nonexpansive mappings. Under suitable conditions some strong convergence theorems are established in uniformly smooth and strictly convex Banachspaces with Kadec-Klee property. The results presented in the paper improve and extend some recent results.

Full Text Available We prove the Hyers-Ulam stability of linear second-order differential equations in complex Banachspaces. 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.

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

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

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 Banachspace, 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

Full Text Available We introduce and study a new system of generalized nonlinear mixed variational inclusions in real -uniformly smooth Banachspaces. We prove the existence and uniqueness of solution and the convergence of some new -step iterative algorithms with or without mixed errors for this system of generalized nonlinear mixed variational inclusions. The results in this paper unify, extend, and improve some known results in literature.

We construct a tensor Banach functor T ? that establishes a correspondence between every projectively admissible Banachspace E over a complete normed field K with a tensor Banach algebra of projective type T ?.

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

In this article, we shall discuss some recent developments and applicationsof the local spectral theory for linear operators on Banachspaces. Specialemphasis will be given to those parts of operator theory, where spectral theory,harmonic analysis, and the theory of Banach algebras overlap and interact.Along this line, we shall present the recent progress of the theory of quotientsand restrictions of decomposable operators, some connections between localspectral theory and the Kato resolvent set, and a general theory of spectralinclusions for certain parts of the spectrum. The abstract theory will be appliedand exemplified in the context of convolution operators induced by measureson a locally compact abelian group G: In particular, we shall investigate thosemeasures on G; for which the corresponding convolution operators on the groupalgebra L1(G) or the measure algebra M(G) are decomposable in the sense ofFoia¸s or have a natural spectrum in the sense of Zafran.1991 M...

The existence of a solution, convergence and stability of the penalty method for variational inequalities with nonsmooth unbounded uniformly and properly monotone operators in Banach spase $B$ are investigated. All the objects of the inequality - the operator A, "the right-hand part" $f$ and the set of constrains $\\Omega $ - are to be perturbed. The stability theorems are formulated in terms of geometric characteristics of the spaces $B$ and $B^*$. The results of this paper are continuity and generalization of the Lions' ones, published earlier in \\cite{l}. They are new even in Hilbert spaces.

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

Full Text Available Abstract in spanish Nosotros consideramos auto aplicaciones ø?1,ø ?2 del disco unitario abierto bien como aplicaciones analíticas ?1, ?2. 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. Abstract in english We consider analytic self-maps ø?1,ø ?2 of the open unit disk as well as analytic maps? 1, ?2. These maps induce differences of weighted composition operators acting between weighted Banachspaces 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.

Full Text Available We consider analytic self-maps ø?1,ø ?2 of the open unit disk as well as analytic maps? 1, ?2. These maps induce differences of weighted composition operators acting between weighted Banachspaces 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 ?1, ?2. 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.

We consider the task of computing an approximate minimizer of the sum of a smooth and a non-smooth convex functional, respectively, in Banachspace. 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 Banachspaces. 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 Banachspaces as well as total-variation-based image restoration in higher dimensions are presented.

[en] We consider the task of computing an approximate minimizer of the sum of a smooth and a non-smooth convex functional, respectively, in Banachspace. 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 Banachspaces. 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 Banachspaces as well as total-variation-based image restoration in higher dimensions are presented

We consider the task of computing an approximate minimizer of the sum of a smooth and non-smooth convex functional, respectively, in Banachspace. 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 Banachspaces. 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 Banachspaces is presented.

Let K be a nonempty closed and convex subset of a real uniformly smooth Banachspace, E, with modulus of smoothness of power type q>1. Let T be a mapping of K into itself, T is an element of C (in the notion of Browder and Petryshyn; and Rhoades). It is proved that the Mann iteration process, under suitable conditions, converges strongly to the unique fixed point of T. If K is also bounded, then the Ishikawa iteration process converges to the fixed point of T. While our theorems generalize important known results, our method is also of independent interest. (author). 14 refs

Full Text Available This article is devoted to the study linear non-autonomous dynamical systems possessing the property of uniform exponential stability. We prove that if the Cauchy operator of these systems possesses a certain compactness property, then the uniform asymptotic stability implies the uniform exponential stability. For recurrent (almost periodic) systems this result is precised. We also show application for different classes of linear evolution equations: ordinary linear differential equations in a Banachspace, retarded and neutral functional differential equations, and some classes of evolution partial differential equations.

Full Text Available It is shown that if X is a uniformly convex Banachspace and S a bounded linear operator on X for which Ã¢Â€Â–IÃ¢ÂˆÂ’SÃ¢Â€Â–=1, then S is invertible if and only if Ã¢Â€Â–IÃ¢ÂˆÂ’12SÃ¢Â€Â–<1. From this it follows that if S is invertible on X then either (i) dist(I,[S])<1, or (ii) 0 is the unique best approximation to I from [S], a natural (partial) converse to the well-known sufficient condition for invertibility that dist(I,[S])<1.

We consider the abstract initial value problem for evolution equations which describe heat convection of incompressible viscous isotropic fluids with the asymmetric stress tensor. It is difficulty in the law of conservation of energy that the dissipation function must be taken into account. This problem has uniquely a mild solution. Moreover, a mild solution of this problem can be a strong or classical solution under appropriate assumptions for initial data. We prove the above properties by the theory of analytic semigroups on Banachspaces.

Full Text Available In this paper we examine a class of nonlinear integral inclusions defined in a separable Banachspace. For this class of inclusions of Volterra type we establish two existence results, one for inclusions with a convex-valued orientor field and the other for inclusions with nonconvex-valued orientor field. We present conditions guaranteeing that the multivalued map that represents the right-hand side of the inclusion is ?-condensing using for the proof of our results a known fixed point theorem for ?-condensing maps.

Full Text Available Let $varphi$ be a positive and non-decreasing function defined on the real half-line and ${mathcal U}$ be a strongly measurable, exponentially bounded evolution family of bounded linear operators acting on a Banachspace and satisfing a certain measurability condition as in Theorem 1 below. We prove that if $varphi$ and ${mathcal U}$ satisfy a certain integral condition (see the relation ef{0.1} from Theorem 1 below) then ${mathcal U}$ is uniformly exponentially stable. For $varphi$ continuous and $mathcal U$ strongly continuous and exponentially bounded, this result is due to Rolewicz. The proofs uses the relatively recent techniques involving evolution semigroup theory.

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

Full Text Available Let ÃŽÂ´X(ÃÂµ) and R(1,X) be the modulus of convexity and the DomÃƒÂnguez-Benavides coefficient, respectively. According to these two geometric parameters, we obtain a sufficient condition for normal structure, that is, a Banachspace X has normal structure if 2ÃŽÂ´X(1+ÃÂµ)>max{(R(1,x)-1)ÃÂµ,1-(1-ÃÂµ/R(1,X)-1)} for some ÃÂµÃ¢ÂˆÂˆ[0,1] which generalizes the known result by Gao and Prus.

It is a longstanding problem whether every contractible Banach algebra is necessarily finite-dimensional. In this note, we confirm this for Banach algebras acting on Banachspaces with the uniform approximation property. This generalizes a result of Paulsen and Smith who proved the same for Banach algebras acting on Hilbert spaces.

Full Text Available Abstract We first prove the existence of a solution of the generalized equilibrium problem (GEP) using the KKM mapping in a Banachspace setting. Then, by virtue of this result, we construct a hybrid algorithm for finding a common element in the solution set of a GEP and the fixed point set of countable family of nonexpansive mappings in the frameworks of Banachspaces. By means of a projection technique, we also prove that the sequences generated by the hybrid algorithm converge strongly to a common element in the solution set of GEP and common fixed point set of nonexpansive mappings. AMS Subject Classification: 47H09, 47H10

We prove a linear operator T acting between l_p-type spaces attains its norm if, and only if, there exists a not weakly null maximizing sequence for T. For 1

We consider the effect of perturbations to a quasi-linear parabolic stochastic differential equation set in a UMD Banachspace $X$. To be precise, we consider perturbations of the linear part, i.e. the term concerning a linear operator $A$ generating an analytic semigroup. We provide estimates for the difference between the solution to the original equation $U$ and the solution to the perturbed equation $U_0$ in the $L^p(\\Omega;C([0,T];X))$-norm. In particular, this difference can be estimated $|| R(\\lambda:A)-R(\\lambda:A_0) ||$ for sufficiently smooth non-linear terms. The work is inspired by the desire to prove convergence of space discretization schemes for such equations. In this article we prove convergence rates for the case that $A$ is approximated by its Yosida approximation, and in a forthcoming publication we consider convergence of Galerkin and finite-element schemes in the case that $X$ is a Hilbert space.

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

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

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

Kuhn-Tucker conditions for mathematical programming problems in Banachspaces partially ordered by cone with empty interior are obtained under strong simultaneity condition. If partial ordered cone has interior point, it is proved that Slater and strong simultaneity conditions are equivalent.

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

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

Full Text Available This paper provide some applications of Pettis integration to differential inclusions in Banachspaces with three point boundary conditions of the form $$ ddot{u}(t) in F(t,u(t),dot u(t))+H(t,u(t),dot u(t)),quad hbox{a.e. } t in [0,1], $$ where $F$ is a convex valued multifunction upper semicontinuous on $Eimes E$ and $H$ is a lower semicontinuous multifunction. The existence of solutions is obtained under the non convexity condition for the multifunction $H$, and the assumption that $F(t,x,y)subset Gamma_{1}(t)$, $H(t,x,y)subset Gamma_{2}(t)$, where the multifunctions $Gamma_{1},Gamma_{2}:[0,1] ightrightarrows E$ are uniformly Pettis integrable.

It is shown that if (X,||.||_X) is a Banachspace with Rademacher type p \\ge 1, then for every integer n there exists an even integer m X, \\Avg_{x,\\e}[||f(x+ m\\e/2)-f(x)}||_X^p] < C(p,X) m^p\\sum_{j=1}^n\\Avg_x[||f(x+e_j)-f(x)||_X^p], where the expectation is with respect to uniformly chosen x \\in Z_m^n and \\e \\in \\{-1,1\\}^n, and C(p,X) is a constant that depends on p and the Rademacher type constant of X. This improves a bound of m < Cn^{3-2/p} that was obtained in [Mendel, Naor 2007]. The proof is based on an augmentation of the "smoothing and approximation" scheme, which was implicit in [Mendel, Naor 2007].

In this paper, we prove that for a unital commutative and finitely generated ring $A$, the group $G= EL_n (A)$ has a fixed point property for affine isometric actions on $B$ if $n \\geq 4$. Here $B$ stands for any $L^p$ space or any Banachspace isomorphic to a Hilbert space. We also verify that the comparison map in degree 2 $\\Psi^2 \\colon H_b^2 (G,B) \\to H^2 (G,B)$ from bounded to usual cohomology is injective, where $G$ and $B$ are same as in above. For our proof, we establish a certain implication from Kazhdan's property (T) to a fixed point property on uniformly convex Banachspaces.

A Banach algebra A is self-induced if the multiplication is an isomorphism from the A-balanced projective tensor-square of A to A. The class of self-induced Banach algebras is a natural generalization of unital Banach algebras, providing a fertile framework for developing homological aspects of unital Banach algebras. Elementary results with applictions to computations of the bounded Hochschild cohomology groups H^1(A,A^*) with emphasis on A=A(X), the approximable operators on a Banachspace X, are given.

We study bundles of Banach algebras ÃÂ€:AÃ¢Â†Â’X, where each fiber Ax=ÃÂ€Ã¢ÂˆÂ’1({x}) is a Banach algebra and X is a compact Hausdorff space. In the case where all fibers are commutative, we investigate how the Gelfand representation of the section space algebra ÃŽÂ“(ÃÂ€) relates to the Gelfand r...

Full Text Available Suppose K is a nonempty closed convex nonexpansive retract of a real uniformly convex Banachspace E with P as a nonexpansive retraction. Let T:KÃ¢Â†Â’E be an asymptotically nonexpansive mapping with {kn}Ã¢ÂŠÂ‚[1,Ã¢ÂˆÂž) such that Ã¢ÂˆÂ‘n=1Ã¢ÂˆÂž(knÃ¢ÂˆÂ’1)0. Starting from arbitrary x1Ã¢ÂˆÂˆK, define the sequence {xn} by x1Ã¢ÂˆÂˆK, zn=P(ÃŽÂ±n''T(PT)nÃ¢ÂˆÂ’1xn+(1Ã¢ÂˆÂ’ÃŽÂ±n'')xn), yn=P(ÃŽÂ±n'T(PT)nÃ¢ÂˆÂ’1zn+(1Ã¢ÂˆÂ’ÃŽÂ±n')xn), xn+1=P(ÃŽÂ±nT(PT)nÃ¢ÂˆÂ’1yn+(1Ã¢ÂˆÂ’ÃŽÂ±n)xn). (i) If the dual E* of E has the Kadec-Klee property, then { xn} converges weakly to a fixed point pÃ¢ÂˆÂˆF(T); (ii) if T satisfies condition (A), then {xn} converges strongly to a fixed point pÃ¢ÂˆÂˆF(T).

Full Text Available Suppose K is a nonempty closed convex nonexpansive retract of a real uniformly convex Banachspace 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)0. Starting from arbitrary x1?K, define the sequence {xn} by x1?K, zn=P(?n''T(PT)n?1xn+(1??n'')xn), yn=P(?n'T(PT)n?1zn+(1??n')xn), xn+1=P(?nT(PT)n?1yn+(1??n)xn). (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).

The convergence of iterative methods for solving nonlinear operator equations in Banachspaces is established from the convergence of majorizing sequences. An alternative approach is developed to establish this convergence by using recurrence relations. For example, the recurrence relations are used in establishing the convergence of Newton's method [L.B. Rall, Computational Solution of Nonlinear Operator Equations, Robert E. Krieger, New York, 1979] and the third order methods such as Halley's, Chebyshev's and super Halley's [V. Candela, A. Marquina, Recurrence relations for rational cubic methods I: the Halley method, Computing 44 (1990) 169-184; V. Candela, A. Marquina, Recurrence relations for rational cubic methods II: the Halley method, Computing 45 (1990) 355-367; J.A. Ezquerro, M.A. Hernandez, Recurrence relations for Chebyshev-type methods, Appl. Math. Optim. 41 (2000) 227-236; J.M. Gutierrez, M.A. Hernandez, Third-order iterative methods for operators with bounded second derivative, J. Comput. Appl. Math. 82 (1997) 171-183; J.M. Gutierrez, M.A. Hernandez, Recurrence relations for the Super-Halley method, Comput. Math. Appl. 7(36) (1998) 1-8; M.A. Hernandez, Chebyshev's approximation algorithms and applications, Comput. Math. Appl. 41 (2001) 433-445 [10

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

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

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

nded but not necessarily isometrical*-isomorphisms of the algebras FS :1. Introduction and preliminaries.Extensive development of non-commutative geometry requires elaboratingof the theory of differential Banach *-algebras, that is, dense *-subalgebrasof C-algebras whose properties in many respects are analogous to the propertiesof algebras of differentiable functions.Blackadar and Cuntz [2] and the authors [12] introduced and studiedvarious classes of differential Banach *-algebras; the most interesting classconsists of D-algebras, that is, dense *-subalgebras A of C-algebras (U; k Delta k)which, in turn, are Banach *-algebras with respect to another norm k Delta k 1and the norms k Delta k and k Delta k 1 on A

Full Text Available We provide a local convergence analysis for a Newton-type method to approximate a locally unique solution of an operator equation in Banachspaces. The local convergence of this method was studied in the elegant work by Werner in [11], using information on the domain of the operator. Here, we use information only at a point and a gamma-type condition [4], [10]. It turns out that our radius of convergence is larger, and more general than the corresponding one in [10]. Moreover the same can hold true when our radius is compared with the ones given in [9] and [11]. A numerical example is also provided

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

Full Text Available We consider a nonlinear Volterra integral equation governed by an m-accretive operator and a multivalued perturbation in a separable Banach. The existence of a continuous selection for the corresponding solution map is proved. The case when the m-accretive operator in the integral inclusion depends on time is also discussed.

Full Text Available We study bundles of Banach algebras ÃÂ€:AÃ¢Â†Â’X, where each fiber Ax=ÃÂ€Ã¢ÂˆÂ’1({x}) is a Banach algebra and X is a compact Hausdorff space. In the case where all fibers are commutative, we investigate how the Gelfand representation of the section space algebra ÃŽÂ“(ÃÂ€) relates to the Gelfand representation of the fibers. In the general case, we investigate how adjoining an identity to the bundle ÃÂ€:AÃ¢Â†Â’X relates to the standard adjunction of identities to the fibers.

We investigate a method for producing concrete convex-transitive Banachspaces. The gist of the method is in getting rid of dissymmetries of a given space by taking a carefully chosen quotient. The spaces of interest here are typically Banach algebras and their ideals. We also investigate the convex-transitivity of ultraproducts and tensor products of Banachspaces.

Full Text Available The article shows the existence of positive solutions for systems of nonlinear singular differential equations with integral boundary conditions on an infinite interval in Banachspaces. Our main tool is the Monch fixed point theorem combined with a monotone iterative technique. In addition, an explicit iterative approximation of the solution is provided.

We consider semilinear evolution equations for which the linear part generates a strongly continuous semigroup and the nonlinear part is sufficiently smooth on a scale of Banachspaces. We show that a class of implicit, A-stable Runge-Kutta methods which includes Gauss-Legendre collocation methods, when applied to such equations, are smooth as maps from open subsets of the highest scale rung into the lowest scale rung. Moreover, under an additional assumption which is, in particular, satisfied in the Hilbert space case, we prove convergence of the time-semidiscretization Our results apply, in particular, to the semilinear wave equation and to the nonlinear Schr\\"odinger equation on the circle.

Full Text Available Let {Xk} be independent random variables with EXk=0 for all k and let {ank:nÃ¢Â‰Â¥1,Ã¢Â€Â‰kÃ¢Â‰Â¥1} be an array of real numbers. In this paper the almost sure convergence of Sn=Ã¢ÂˆÂ‘k=1nankXk, n=1,2,Ã¢Â€Â¦, to a constant is studied under various conditions on the weights {ank} and on the random variables {Xk} using martingale theory. In addition, the results are extended to weighted sums of random elements in Banachspaces which have Schauder bases. This extension provides a convergence theorem that applies to stochastic processes which may be considered as random elements in function spaces.

Full Text Available Abstract in english We provide a local convergence analysis for a Newton-type method to approximate a locally unique solution of an operator equation in Banachspaces. The local convergence of this method was studied in the elegant work by Werner in [11], using information on the domain of the operator. Here, we use information only at a point and a gamma-type condition [4], [10]. It turns out that our radius of convergence is larger, and more general than the corresponding one in [10]. More (more) over the same can hold true when our radius is compared with the ones given in [9] and [11]. A numerical example is also provided

Let A:D(A)\\to E be an infinitesimal generator either of an analytic compact semigroup or of a contractive C_0-semigroup of linear operators acting in a Banachspace E. In this paper we give both necessary and sufficient conditions for bifurcation of $T$-periodic solutions for the equation x'=Ax+f(t,x)+e g(t,x,e) from a k-parameterized family of T-periodic solutions of the unperturbed equation corresponding to e=0. We show that by means of a suitable modification of the classical Mel'nikov approach we can construct a bifurcation function and to formulate the conditions for the existence of bifurcation in terms of the topological index of the bifurcation function. To do this, since the perturbation term g is only Lipschitzian we need to extend the classical Lyapunov-Schmidt reduction to the present nonsmooth case.

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 Banachspace 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.

We prove that if $X$ is a real Banachspace, with $\\dim X\\geq 3$, which contains a subspace of codimension 1 which is 1-complemented in $X$ and whose group of isometries is almost transitive then $X$ is isometric to a Hilbert space. This partially answers the Banach-Mazur rotation problem and generalizes some recent related results.

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.

In this erratum, we recover the results from an earlier paper of the author's which contained a gap. Specifically, we prove that if X is a Banachspace with an unconditional basis and admits a C^{p}-smooth, Lipschitz bump function, and Y is a convex subset of X, then any uniformly continuous function f: Y->R can be uniformly approximated by Lipschitz, C^{p}-smooth functions K:X->R. Also, if Z is any Banachspace and f:X->Z is L-Lipschitz, then the approximates K:X->Z can be chosen CL-Lipschitz and C^{p}-smooth, for some constant C depending only on X.

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

We give an abstract definition, similar to the axioms of a Stein manifold, of a class of complex Banach manifolds in such a way that a manifold belongs to the class if and only if it is biholomorphic to a closed split complex Banach submanifold of a separable Banachspace.

We prove that if a unital Banach algebra $A$ is the dual of a Banachspace $\\pd{A}$, then the set of weak* continuous states is weak* dense in the set of all states on $A$. Further, weak* continuous states linearly span $\\pd{A}$.

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 Banachspace 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.

Let $X$ be a real Banachspace with an unconditional basis (e.g., $X=\\ell_2$ Hilbert space), $\\Omega\\subset X$ open, $M\\subset\\Omega$ a closed split real analytic Banach submanifold of $\\Omega$, $E\\to M$ a real analytic Banach vector bundle, and ${\\Cal A}^E\\to M$ the sheaf of germs of real analytic sections of $E\\to M$. We show that the sheaf cohomology groups $H^q(M,{\\Cal A}^E)$ vanish for all $q\\ge1$, and there is a real analytic retraction $r:U\\to M$ from an open set $U$ with $M\\subset U\\subset\\Omega$ such that $r(x)=x$ for all $x\\in M$. Some applications are also given, e.g., we show that any infinite dimensional real analytic Hilbert submanifold of separable affine or projective Hilbert space is real analytically parallelizable.

In the theory of ordered spaces and in microeconomic theory two important notions, the notion of the base for a cone which is defined by a continuous linear functional and the notion of the budget set are equivalent. In economic theory the maximization of the preference relation of a consumer on any budget set defines the demand correspondence which at any price vector indicates the preferred vectors of goods and this is one of the fundamental notions of this theory. Contrary to the finite-dimensional economies, in the infinite-dimensional ones, the existence of the demand correspondence is not ensured. In this article we show that in reflexivespaces (and in some other classes of Banachspaces), there are only two classes of closed cones, i.e. cones whose any budget set is bounded and cones whose any budget set is unbounded. Based on this dichotomy result, we prove that in the first category of these cones the demand correspondence exists and that it is upper hemicontinuous. We prove also a characterization of reflexivespaces based on the existence of the demand correspondences.

[en] The notion of a 2-Banach algebra is introduced and its structure is studied. After a short discussion of some fundamental properties of bivectors and tensor product, several classical results of Banach algebras are extended to the 2-Banach algebra case. A condition under which a 2-Banach algebra becomes a Banach algebra is obtained and the relation between algebra of bivectors and 2-normed algebra is discussed. 11 refs

In the present work we provide a variety of examples of HI Banachspaces containing no reflexive subspace and we study the structure of their duals as well as the spaces of their linear bounded operators. Our approach is based on saturated extensions of ground sets and the method of attractors.

In this paper we define the directional differentiability along a dense linear subspace D of a Banachspace E and study the critical values of D-differentiable functionals on surfaces in E. (author). 11 refs.

En este trabajo se estudia la perturbación de la inversa generalizada grupo en el ámbito 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...

Castro González, Nieves; Vélez Cerrada, José Ygnacio

Full Text Available We present two new forms in which the Frechet differential of a power series in a unitary Banach algebra can be expressed in terms of absolutely convergent series involving the commutant $C(T) : A \\rightarrow [A,T]$. Then we apply the results to study series of vector-valued functions on domains in Banachspaces and to the analytic functional calculus in a complex Banachspace.

The notion of a 2-Banach algebra is introduced and its structure is studied. After a short discussion of some fundamental properties of bivectors and tensor products, several classical results of Banach algebras are extended to the 2-Banach algebra case. ...

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

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.

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

We study the structure of biprojective Banach algebras. In contrast to earlier results of Selivanov, we admit the presence of nilpotent ideals in the algebras under consideration, and the structure theorem covers almost all known examples. As a corollary, we obtain a complete classification of finite-dimensional biprojective Banach algebras. A major role in the proof is played by the approximation property for certain Banachspaces related to the algebras under consideration.

Aristov, O Yu [Obninsk State Technical University for Nuclear Power Engineering, Obninsk, Kaluzhskaya obl. (Russian Federation)

[en] We study the structure of biprojective Banach algebras. In contrast to earlier results of Selivanov, we admit the presence of nilpotent ideals in the algebras under consideration, and the structure theorem covers almost all known examples. As a corollary, we obtain a complete classification of finite-dimensional biprojective Banach algebras. A major role in the proof is played by the approximation property for certain Banachspaces related to the algebras under consideration

We study the structure of biprojective Banach algebras. In contrast to earlier results of Selivanov, we admit the presence of nilpotent ideals in the algebras under consideration, and the structure theorem covers almost all known examples. As a corollary, we obtain a complete classification of finite-dimensional biprojective Banach algebras. A major role in the proof is played by the approximation property for certain Banachspaces related to the algebras under consideration.

We construct a crossed product Banach algebra from a Banach algebra dynamical system $(A,G,\\alpha)$ and a given uniformly bounded class $R$ of continuous covariant Banachspace representations of that system. If $A$ has a bounded left approximate identity, and $R$ consists of non-degenerate continuous covariant representations only, then the non-degenerate bounded representations of the crossed product are in bijection with the non-degenerate $R$-continuous covariant representations of the system. This bijection, which is the main result of the paper, is also established for involutive Banach algebra dynamical systems and then yields the well-known representation theoretical correspondence for the crossed product $C^*$-algebra as commonly associated with a $C^*$-algebra dynamical system as a special case. Taking the algebra $A$ to be the base field, the crossed product construction provides, for a given non-empty class of Banachspaces, a Banach algebra with a relatively simple structure and with the property...

Full Text Available We introduce new notions of approximate amenability for a Banach algebra A. A Banach algebra A is n-approximately weakly amenable, for n ? N, if every continuous derivation from A into the n-th dual space A(n) is approximately inner. First we examine the relation between m-approximately weak amenability and n-approximately weak amenability for distinct m,n ? N. Then we investigate (2n+1)-approximately weak amenability of module extension Banach algebras. Finally, we give an example of a Banach algebra that is 1-approximately weakly amenable but not 3-approximately weakly amenable.

Let $K$ be an ultrametric complete field and let $E$ be an ultrametric space. Let $A$ be the Banach $K$-algebra of bounded continuous functions from $E$ to $K$ and let $B$ be the Banach $K$-algebra of bounded uniformly continuous functions from $E$ to $K$. Maximal ideals and continuous multiplicativ...

We introduce new notions of approximate amenability for a Banach algebra A. A Banach algebra A is n-approximately weakly amenable, for n ? N, if every continuous derivation from A into the n-th dual space A(n) is approximately inner. First we examine the relation between m-approximate...

this paper, we shall solve Problem 1.1 completely and also provide constructive formulas forthe inverses in terms of minors, which will be useful for numerical calculations. In the proof, we shall seethat the Gelfand transform provides a right tool for Banach algebras just as the quotient field plays a crucialrole for integral domains. They both link the ring with a field effectively, so that one can utilize manynice properties from a field. The paper is arranged as follows. In the second section, we present necessaryand sufficient conditions for the existence of a reflexive g-inverse. In the third section, we give necessaryand sufficient conditions for the Moore-Penrose inverses. All examples and applications are put in the lastsection.ACKNOWLEDGMENTS

Full Text Available Suppose X and Y are reflexiveBanachspaces. If K(X,Y), the space of all compact linear operaters from X to Y is an M-ideal in L(X,Y), the space of all bounded linear operators from X to Y, then the second dual space K(X,Y)** of K(X,Y) is isometrically isomorphic to L(X,Y).

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

We consider weighted algebras of holomorphic functions on a Banachspace. We determine conditions on a family of weights that assure that the corresponding weighted space is an algebra or has polynomial Schauder decompositions. We study the spectra of weighted algebras and endow them with an analytic structure. We also deal with composition operators and algebra homomorphisms, in particular to investigate how their induced mappings act on the analytic structure of the spectrum. Moreover, a Banach-Stone type question is addressed.

[en] 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 Lie–Jordan 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 Lie–Jordan 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)

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 Lie-Jordan 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 Lie-Jordan 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.

In the present article we prove a fixed point theorem for reflections of compact convex sets and give a new characterization of state space of JB-algebras among compact convex sets. Namely they are exactly those compact convex sets which are strongly spectral and symmetric.

Full Text Available Let D be a derivation on a Banach algebra; by using the operator D2, we give necessary and sufficient conditions for the separating ideal of D to be nilpotent. We also introduce an ideal M(D) and apply it to find out more equivalent conditions for the continuity of D and for nilpotency of its separating ideal.

An element $g$ of a group is called {\\em reversible} if it is conjugate in the group to its inverse. In this paper we review some results about the structure of groups involving the reversible elements and we pose some questions about groups associated to a Banach algebra.

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.

ollows easily from the continuity ofcharacters that every homomorphism ` : A !B from a Banach algebra A into a commutative,semisimple Banach algebra B is continuous.A closely related result is Johnson'suniqueness-of-norm-theorem: every semisimpleBanach algebra has a unique complete algebranorm. For lovely alternative proofs ofthis theorem, see [1] and [13]. There arenon-semsimple, commutative Banach algebraswhich have a unique complete algebranorm. For example, this is true of the convolutionalgebras L(R; !), where ! is aweight function on R(see [4], x5.2). Onthe other hand, there are even commutativeBanach algebras with a one-dimensional (Jacobson)radical which do not have a uniquecomplete algebra norm (see [4], x5.1). Neverthelessthere are striking open questions inthis area: we do not know whether a commutativeBanach algebra which is an integraldomain necessarily has a unique complete algebranorm; the question is also open for Banachalgebras with

Full Text Available Abstract in spanish Se estudia el módulo de receptividad de los módulos de Banach. Esta es una generalización natural de la receptividad de Johnson de las álgebras de Banach. Como ejemplo se muestra que para un grupo abeliano discreto G l p(G) es receptivo como un G l p(G)- módulo, si y sólo si G es receptivo, donde l¹(G) es un álgebra de Banach con producto punto. Abstract in english We study the module amenability of Banach modules. This is a natural generalization of Johnson?s amenability of Banach algebras. As an example we show that for a discrete abelian group G, l p(G) is amenable as an l¹(G)-module if and only if G is amenable, where l¹(G) is a Banach algebra with pointwise multiplication.

Full Text Available We study the module amenability of Banach modules. This is a natural generalization of Johnson’s amenability of Banach algebras. As an example we show that for a discrete abelian group G, l p(G) is amenable as an l¹(G)-module if and only if G is amenable, where l¹(G) is a Banach algebra with pointwise multiplication.Se estudia el módulo de receptividad de los módulos de Banach. Esta es una generalización natural de la receptividad de Johnson de las álgebras de Banach. Como ejemplo se muestra que para un grupo abeliano discreto G l p(G) es receptivo como un G l p(G)- módulo, si y sólo si G es receptivo, donde l¹(G) es un álgebra de Banach con producto punto.

We introduce and study the notion of null-orbit reflexivity, which is a slight perturbation of the notion of orbit-reflexivity. Positive results for orbit reflexivity and the recent notion of $\\mathbb{C}$-orbit reflexivity both extend to null-orbit reflexivity. Of the two known examples of operators that are not orbit-reflexive, one is null-orbit reflexive and the other is not. The class of null-orbit reflexive operators includes the classes of hyponormal, algebraic, compact, strictly block-upper (lower) triangular operators, and operators whose spectral radius is not 1. We also prove that every polynomially bounded operator on a Hilbert space is both orbit-reflexive and null-orbit reflexive.

We introduce a property of Banachspaces called uniform convex-transitivity, which falls between almost transitivity and convex-transitivity. We will provide examples of uniformly convex-transitive spaces. This property behaves nicely in connection with some Banach-valued function spaces. As a consequence, we obtain new examples of convex-transitive Banachspaces.

In this paper, we prove the Hyers-Ulam-Rassias stability of homomorphisms in quasi-Banach algebras associated to the Pexiderized Cauchy functional equation. This is applied to investigate homomorphisms between quasi-Banach algebras. The concept of Hyers-Ulam-Rassias stability originated from Th.ME Rassias' stability theorem that appeared in his paper [Th.M. Rassias, On the stability of the linear mapping in Banachspaces, Proc. Amer. Math. Soc. 72 (1978) 297-300].

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

Recent studies by Diamond and Markham 1,2 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 by von Baumgarten and Thümler 3 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.

We study conditions on a Banach frame that ensures the validity of a reconstruction formula. In particular, we show that any Banach frames for (a subspace of) $L_p$ or $L_{p,q}$ ($1\\le p < \\infty$) with respect to a solid sequence space always satisfies an unconditional reconstruction formula. The existence of reconstruction formulae allows us to prove some James-type results for atomic decompositions: an unconditional atomic decomposition (or unconditional Schauder frame) for $X$ is shrinking (respectively, boundedly complete) if and only if $X$ does not contain an isomorphic copy of $\\ell_1$ (respectively, $c_0$).

Suppose A is a Banach algebra and suppose is an approximate ring derivation in the sense of Hyers-Ulam-Rassias. This stability phenomenon was introduced for the first time in the subject of functional equations by Th.M. Rassias [Th.M. Rassias, On the stability of the linear mapping in Banachspaces, Proc. Amer. Math. Soc. 72 (1978) 297-300]. If A has an approximate identity, or if A is semisimple and commutative, then we prove that f is an exact ring derivation.

A theory of reduction of Lie-Jordan Banach algebras with respect to either a Jordan ideal or a Lie-Jordan subalgebra is presented. This theory is compared with the standard reduction of C*-algebras of observables of a quantum system in the presence of quantum constraints. It is shown that the later corresponds to the particular instance of the reduction of Lie-Jordan Banach algebras with respect to a Lie-Jordan subalgebra as described in this paper. The space of states of the reduced Lie-Jordan Banach algebras is described in terms of equivalence classes of extensions to the full algebra and their GNS representations are characterized in the same way. A few simple examples are discussed that illustrates some of the main results.

Full Text Available ??C*-????????Banach*-??????????????C*-??????????????*-???????Banach*-????????????????????????????????For C*-algebras and , we discuss some properties of the Banach*-algebra . Then, we prove that the operator space projective tensor product of C*-algebras preserves *-homomorphism and a universal property of Banach*-algebra will be given. At last, a characterization of the convergence property of dual space is also obtained.

this paper, we always assume that B is a complex commutative Banach algebra withidentity e, and M the maximal ideal space of B endowed with the Gelfand topology. We recall that a matrixA 2 Bis regular if there exists a matrix G 2 Bsatisfying the following equation:(1) AGA = A

this paper is the interplay between order and lattice structure, commutativity,existence of square roots, and monotonicity of powers, in the real part (the hermitianelements) of a unital hermitian Banach *algebra.These questions first appeared in the context of operators on Hilbert space. Lowner[Lo] established the monotonicity of the p

Properties of a virtual cathode in a pulsed ion diode composed of and insulator-mesh anode and a metal-mesh cathode were studied experimentally at anode voltages below 350 kV. Potential distribution in the virtual cathode side was measured with an insulated electrostatic potential probe, and ion beam currents in virtual and real cathode sides were measured with biased ion collectors. Experimental results are given for the space and time behaviors of the anode plasma and the virtual cathode which starts to grow first from a region near a periphery of the metal anode frame and extends over the central region near the anode surface. A loss parameter for the electron current accompanied with the ion beam at the virtual cathode was evaluated from the measured electron current values by using relations derived from the one-dimensional Child-Langmuir theory applied to the reflex triode. The ion beam accompanies a considerable amount of electron current, and this influences the stability of the virtual cathode; this perturbation results in variations of ion current with time. Experimental results for space potentials in the emitted ion beam and the total current flowing in the space of the virtual cathode side are also given, suggesting an existence of high energy electrons of several keV accelerated by positive space potential of the ion beam.

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.

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.

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.

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

[en] 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)

We study the structure of generators of the Banach algebras (Wp(n)[0,1],*) and (Wp(n)[0,1],?), where * denotes the usual convolution and ? the so-called Duhamel product. We also give a new characterization of a special class of composition operators acting in the Sobolev space Wp(n)[0,1] by the formula (C?f)(x) = f(?(x)).

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

We continue our work [E. Kaniuth, A.T. Lau, J. Pym, On [phi]-amenability of Banach algebras, Math. Proc. Cambridge Philos. Soc. 144 (2008) 85-96] in the study of amenability of a Banach algebra A defined with respect to a character [phi] of A. Various necessary and sufficient conditions of a global and a pointwise nature are found for a Banach algebra to possess a [phi]-mean of norm 1. We also completely determine the size of the set of [phi]-means for a separable weakly sequentially complete Banach algebra A with no [phi]-mean in A itself. A number of illustrative examples are discussed.

Full Text Available 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 corresponds a unique -ring homomorphism near to for all .

The purpose of this paper is to study the structure of reflexive sheaves over projective spaces through hyperplane sections. We give a criterion for a reflexive sheaf to split into a direct sum of line bundles. An application to the theory of free hyperplane arrangements is also given.

> D(A) ! C has a holomorphicextension to A 0 .In this definition we consider the identitycomponentofA inv rather thanA inv since if A inv is not connected the holomorphic function on A inv whichis 1 on one of the components and 0 on the others has no holomorphicextension to A 0 . It follows from Theorem 3 given in the next section (orsee [12, Theorem 3]) that our definition is no more stringent when the rangeof f is allowed to be any Banachspace.12 LAWRENCE A. HARRISEvery finite dimensional Banach algebra A has the removable singularitypropertyby the classical Riemann removable singularities theorem [6,p. 30] and the characterization of the singular elements of A as thosewith determinant zero. (Define the determinantofanelementofA as thedetermina

holomorphic function f : D(A) ! C has a holomorphicextension to A 0 .In this definition we consider the identity component of A inv rather thanA inv since if A inv is not connected the holomorphic function on A inv whichis 1 on one of the components and 0 on the others has no holomorphicextension to A 0 . It follows from Theorem 3 given in the next section (orsee [12, Theorem 3]) that our definition is no more stringent when the rangeof f is allowed to be any Banachspace.12 LAWRENCE A. HARRISEvery finite dimensional Banach algebra A has the removable singularityproperty by the classical Riemann removable singularities theorem [6,p. 30] and the characterization of the singular elements of A as those

Quasi-multipliers for a Hilbert C*-bimodule V were introduced by Brown, Mingo and Shen 1994 as a certain subset of the Banach bidual module V**. We give another (equivalent) definition of quasi-multipliers for Hilbert C*-bimodules using the centralizer approach and then show that quasi-multipliers are, in fact, universal (maximal) objects of a certain category. We also introduce quasi-multipliers for bimodules in Kasparov's sense and even for Banach bimodules over C*-algebras, provided these C*-algebras act non-degenerately. A topological picture of quasi-multipliers via the quasi-strict topology is given. Finally, we describe quasi-multipliers in two main situations: for the standard Hilbert bimodule l_2(A) and for bimodules of sections of Hilbert C*-bimodule bundles over locally compact spaces.

Let $\\mathcal{I,J}$ be symmetric quasi-Banach ideals of compact operators on an infinite-dimensional complex Hilbert space $H$, let $\\mathcal{J:I}$ be a space of multipliers from $\\mathcal{I}$ to $\\mathcal{J}$. Obviously, ideals $\\mathcal{I}$ and $\\mathcal{J}$ are quasi-Banach algebras and it is clear that ideal $\\mathcal{J}$ is a bimodule for $\\mathcal{I}$. We study the set of all derivations from $\\mathcal{I}$ into $\\mathcal{J}$. We show that any such derivation is automatically continuous and there exists an operator $a\\in\\mathcal{J:I}$ such that $\\delta(\\cdot)=[a,\\cdot]$, moreover $\\|a\\|_{\\mathcal{B}(H)}\\leq\\|\\delta\\|_\\mathcal{I\\to J}\\leq 2C\\|a\\|_\\mathcal{J:I}$, where $C$ is the modulus of concavity of the quasi-norm $\\|\\cdot\\|_\\mathcal{J}$. In the special case, when $\\mathcal{I=J=K}(H)$ is a symmetric Banach ideal of compact operators on $H$ our result yields the classical fact that any derivation $\\delta$ on $\\mathcal{K}(H)$ may be written as $\\delta(\\cdot)=[a,\\cdot]$, where $a$ is some bounded operator...

Introduces the theory of commutative Banach algebras. This book offers chapters on Gelfand's theory, regularity and spectral synthesis. It emphasises on applications in abstract harmonic analysis and on treating many special classes of commutative Banach algebras, such as uniform algebras, group algebras and Beurling algebras, and tensor products

Full Text Available Suppose A is a Banach algebra without order. We show that an approximate multiplier T:AÃ¢Â†Â’A is an exact multiplier. We also consider an approximate multiplier T on a Banach algebra which need not be without order. If, in addition, T is approximately additive, then we prove the Hyers-Ulam-Rassias stability of T.

The concept of ‘varieties of Banach algebras’ was introduced by the author (Quart. J. Math. Oxford (2), 27 (1976), 481-487). Here we develop the theory, producing analogues of the ‘relatively free’ objects in varieties of universal algebras. We take as a test question the problem of describing all varieties which are closed under bicontinuous isomorphisms (i.e. varieties which are also semivarieties), and show that this may be answered easily with the aid of these new concepts. (The answer is, as expected, just those varieties which are ‘algebraically defined’.)

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

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

In this paper we prove, among other things, that a semi-simple and topologically simple Banach algebra which has an identity and contains a non-zero finite-dimensional element is itself a finite-dimensional algebra.

Full Text Available Let A1, A2 be commutative semisimple Banach algebras and A1Ã¢ÂŠÂ—Ã¢ÂˆÂ‚A2 be their projective tensor product. We prove that, if A1Ã¢ÂŠÂ—Ã¢ÂˆÂ‚A2 is a group algebra (measure algebra) of a locally compact abelian group, then so are A1 and A2. As a consequence, we prove that, if G is a locally compact abelian group and A is a comutative semi-simple Banach algebra, then the Banach algebra L1(G,A) of A-valued Bochner integrable functions on G is a group algebra if and only if A is a group algebra. Furthermore, if A has the Radon-Nikodym property, then the Banach algebra M(G,A) of A-valued regular Borel measures of bounded variation on G is a measure algebra only if A is a measure algebra.

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

It is shown that the tensor Banach functor of projective typehat{T}K [1] corresponding to the complete normed field K is quasiidempotent on infinite-dimensional l 1 spaces, i.e., 11232_2005_Article_BF01018845_TeX2GIFE1.gif hat{T}K (? K (hat{T}K (l_1 (M.K)))) \\cong hat{T}_K (l_1 (M.K)). where M is an infinite set and ? K is the forgetful functor. An l 1 realization of the Banach algebrahat{T}K (l_1 (M.K)) is constructed.

Let $\\cal A$ be a Banach algebra. Then $\\cal A^{**}$ the second dual of $\\cal A$ is a Banach algebra with first (second) Arens product. We study the Arens products of $\\cal A^{4}(=({\\cal A^{**}})^{**}).$ We fined some conditions on $\\cal A^{**}$ to be a left ideal in $\\cal A^{4}.$ We fined the biggest two sided ideal $I$ of ${\\cal A},$ in which $I$ is a left (right) ideal of ${\\cal A}^{**}$.

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.

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

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

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 Köthe 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)).

Foralewski Pawe?; Hudzik Henryk; Kaczmarek Rados?aw; Krbec Miroslav

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 Köthe 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)).

Pawe? Foralewski; Henryk Hudzik; Rados?aw Kaczmarek; Miroslav Krbec

Full Text Available In this paper, we prove the Hyers-Ulam-Rassias stability of isometries and of homomorphisms for additive functional equations in quasi-Banach algebras. This is applied to investigate isomorphisms between quasi-Banach algebras.

We prove a Gelfand Representation type of theorem, by showing that the set $C_s(X)$ of continuous bounded (real or complex valued) functions with separable support on a locally separable metrizable space $X$ (provided with the supremum norm) is a Banach algebra, isometrically isomorphic to $C_0(Y)$, for some unique (up to homeomorphism) locally compact Hausdorff space $Y$. The space $Y$, which we explicitly construct as a subspace of the Stone-\\v{C}ech compactification of $X$, is countably compact, and if $X$ is non--separable, is moreover non--normal; in addition $C_0(Y)=C_{00}(Y)$. When the underlying field of scalars is the complex numbers, the space $Y$ coincides with the spectrum of the ${C}^*$--algebra $C_s(X)$. Further, we find the dimension of the algebra $C_s(X)$.

Full Text Available An extension of the Helson-Edwards theorem for the group algebras to Banach modules over commutative Banach algebras is given. This extension can be viewed as a generalization of Liu-Rooij-Wang's result for Banach modules over the group algebras.

Let $\\mathcal{M}$ be a von Neumann algebra equipped with a faithful normal semi-finite trace $\\tau$ and let $S_0(\\tau)$ be the algebra of all $\\tau$-compact operators affiliated with $\\mathcal{M}$. Let $E(\\tau)\\subseteq S_0(\\tau)$ be a symmetric operator space (on $\\mathcal{M}$) and let $\\mathcal{E}$ be a symmetrically-normed Banach ideal of $\\tau$-compact operators in $\\mathcal{M}$. We study (i) derivations $\\delta$ on $\\mathcal{M}$ with the range in $E(\\tau)$ and (ii) derivations on the Banach algebra $\\mathcal{E}$. In the first case our main results assert that such derivations are continuous (with respect to the norm topologies) and also inner (under some mild assumptions on $E(\\tau)$). In the second case we show that any such derivation is necessarily inner when $\\mathcal{M}$ is a type $I$ factor. As an interesting application of our results for the case (i) we deduce that any derivation from $\\mathcal{M}$ into an $L_p$-space, $L_p(\\mathcal{M},\\tau)$, ($1

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

In this activity, learners will perform various investigations to understand the vestibular-ocular reflex and learn about the importance of visual cues in maintaining balance. During the two-part activity, learners will compare the stability of a moving image under two conditions as well as compare the effects of rotation on the sensation of spinning under varying conditions. This lesson guide includes background information, review and critical thinking questions with answers, and handouts. Educators can also use this activity to discuss how the brain functions in space and how researchers study the vestibular function in space.

Marlene Y. Macleish, Ed D.; Bernice R. Mclean, M. E.

In this work we present an extension to arbitrary unital Banach algebras of a result due to Phillips [R.S. Phillips, Spectral theory of semigroups of linear operators, Trans. Amer. Math. Soc. 71 (1951) 393-415] (Theorem 1.1) which provides sufficient conditions assuring the uniform continuity of strongly continuous semigroups of linear operators. It implies that, when dealing with the algebra of bounded operators on a Banachspace, the conditions of Phillips's theorem are also necessary. Moreover, it enables us to derive necessary and sufficient conditions in terms of essential spectra which guarantee the uniform continuity of strongly continuous semigroups. We close the paper by discussing the uniform continuity of strongly continuous groups acting on Banachspaces with separable duals such that, for each , the essential spectrum of T(t) is a finite set.

We deal with the question of whether or not the p-convexified couple (X_0^{(p)},X_1^{(p)}) is a Calderon couple under the assumption that (X_0,X_1) is a Calderon couple of Banach lattices on some measure space. In this preliminary version of the paper we find that the answer is affirmative in the simple case where X_0 and X_1 are sequence spaces and an additional "positivity" assumption is imposed regarding (X_0,X_1). We also prove a quantitative version of the result with appropriate norm estimates. In future versions of this paper we plan to deal with other and more general cases of these results.

We consider normed and Banach algebras satisfying a condition topologicallyanalogous to bounded index for rings. We investigate stabilityproperties, prove a topological version of a theorem of Jacobson, and findin many cases co-incidence with well-known finiteness properties.1 IntroductionAn element a of a ring R is nilpotent if an= 0 for some n#N, and R is ofbounded index if there is some N#N with aN= 0 for all nilpotent a#R. Suchrings have attracted several authors, for example Jacobson [6] and Klein [9], andit seems natural to consider topological analogues of these rings in the context ofBanach algebras. We pursue such an analogy here in the spirit of P. G. Dixon'swork on topologically nilpotent Banach algebras.For an element a of a normed algebra A we write #(a) for the spectrum of aandr(a) = limn## #an#1/nwhich is, of course, the spectral radius when A is a Banach algebra. If r(a) = 0we will say that a is topologically nilpotent. We d...

Full Text Available Problem statement: In this study, we introduce the concept of a partial ternary derivation from A1 Ã?â?¢â?¢â?¢Ã? An into B, where A1, A2â?¢â?¢â?¢, An and B are ternary algebras. Conclusion/Recommendations: We prove the generalized Hyers-Ulam stability of partial ternary derivations in Banach ternary algebras.

M. Eshaghi; M. B. Savadkouhi; M. Bidkham; C. Park; J. R. Lee

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

M. Eshaghi; M. B. Savadkouhi; M. Bidkham; C. Park; J. R. Lee

Full Text Available It is shown that if the socle soc(A) of a semisimple Banach algebra A is norm-closed, then soc(A) is already finite dimensional. The proof makes use of the Al-Moajil theorem. However it is remarked that our main theorem is an extension of the Al-Moajil's.

[en] 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, ?f, ?f), where Hf is a Hilbert space with scalar product denoted by: , ?f is a representation of A into L(Hf), the space of bounded linear operators on Hf, ?f is a cyclic vector in Hf, such that: f(x)=f(x)?f, ?f >, for all x is an element of A. In this result, the existence of a (multiplicative) involution on A, is central. The aim of this paper is to show that such a construction may be performed for a non-involutive Banach algebra, to obtain a similar triple (H, ?, ?) as above. Moreover, this procedure indeed enables us to associate to the topological dual of any Banachspace, 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

In this dissertation I establish that a broad class of Banach *-algebras of infinite integral operators, defined by the property that the kernels of the elements of the algebras possess subexponential off-diagonal decay, is inverse closed in the Banachspace of bounded linear operators on the Hilbert space of square-integrable functions. I also show that the algebras under consideration are symmetric. In the second part of this dissertation, I present the results of the IEEE Transactions on Communications paper written jointly by Thomas Strohmer and me. We develop a comprehensive framework for the design of orthogonal frequency-division multiplexing (OFDM) systems, using techniques from Gabor frame theory, sphere-packing theory, representation theory, and the Heisenberg group.

The concept of associative ultraprime algebras was developed byM. Mathieu who also showed that it is equivalent to a certain norm estimatewhich we call uniform primeness. The topic was further pursued by severalauthors in both associative and Jordan Banach algebras. In the present notewe give a formal definition of uniformly prime Banach Lie algebra and provethat classical Banach Lie algebras of compact operators, in the sense of de laHarpe, are uniformly prime.1.

We show that the entire cyclic cohomology of Banach algebras definedby Connes has the simplicial normalization property. A key tool in the proof is thenotion and properties of supertraces on the Cuntz algebra QA. As an example offurther applications of this technique we give a proof of the homotopy invariance ofentire cyclic cohomology.Key words Simplicial normalization, homotopy invariance, supertraces, Cuntz algebra,entire cyclic cohomology.1 IntroductionOne of the basic features of the non-commutative geometry introduced in the fundamentalwork of Connes [Co1, Co3] is that in order to have a good analogue ofthe de Rham homology for non-commutative spaces one needs to introduce cycliccohomology, or more generally, theories of cyclic type, like periodic cyclic cohomology.In particular, the periodic cyclic cohomology is the natural target for the Cherncharacter map from K -homology. In the `finite dimensional' situation, the K -cyclesare described by means of p-summab...

In this paper, we have proved an existence results for local asymptotic attractivity and existence of asymptotic stability of solutions for nonlinear functional differential equations in Banach algebras.

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

Let A1, A2 be commutative semisimple Banach algebras and A1Ã¢ÂŠÂ—Ã¢ÂˆÂ‚A2 be their projective tensor product. We prove that, if A1Ã¢ÂŠÂ—Ã¢ÂˆÂ‚A2 is a group algebra (measure algebra) of a locally compact abelian group, then so are A1 and A2. As a consequence, we prove that, if G is a locally compact...

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

Full Text Available Given a quasi-nilpotent Banach algebra A, we will use the results of Seddighin [2], to study the properties of elements which belong to a proper closed two sided ideal of AÃ‚Â¯ and AÃ‚Â¯Ã‚Â¯. Here AÃ‚Â¯ is the extension of A to a Banach Algebra with identity.

It is well known that there are no nonzero linear derivations on complex commutative semisimple Banach algebras. In this paper we prove the following extension of this result. Let ?$A$? be a complex semisimple Banach algebra and let ?$D: A to A$? be a linear mapping satisfying the relation ?$D(x^2) ...

Given a quasi-nilpotent Banach algebra A, we will use the results of Seddighin [2], to study the properties of elements which belong to a proper closed two sided ideal of AÃ‚Â¯ and AÃ‚Â¯Ã‚Â¯. Here AÃ‚Â¯ is the extension of A to a Banach Algebra with identity.

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

We investigate the following functional inequality: Ã¢Â€Â–f(x)+f(y)+f(z)Ã¢Â€Â–Ã¢Â‰Â¤Ã¢Â€Â–f(x+y+z)Ã¢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.

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

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

In order to deal with semigroups on Banachspaces which are not strongly continuous we introduce the concept of bi-continuous semigroups on spaces with two topologies. To that purpose we consider Banachspaces with an aditional locally convex topology tau which is coarser than the norm topology and ...

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

The weak spectral mapping theorem for bounded (and for nonquasianalyticallygrowing) C 0 -groups is re-proved by means of Banach algebrahomomorphisms.1. IntroductionLet X be a Banachspace and A be a generator of a C 0 -group on X . It is knownthat if the group is bounded (or more generally, if it has non-quasianalitic growth)then the weak spectral mapping theorem holds:oe(eAt) = eoe(A)t; t 2R:It is also known that the growth condition cannot be weakened in general. ForC 0 Gammasemigroups only the inclusionoe(eAt) oe eoe(A)t; t 0holds in general (except of some special cases, e.g. analytic semigroups). For asystematic treatment (and references) of the spectral mapping theorem we refer tothe monographs [3], [7].In this paper we will present a proof of the weak spectral mapping theorem forbounded C 0 -groups in the framework of Banach algebras and show that the sameproof goes through for groups with non-quasianalytic growth. We will use a notion...

It is proved that there exists a separable reflexiveBanachspace W that contains an isomorphic image of every separable superreflexive Banachspace. This gives the affirmative answer on one J. Bourgain's question

Let $X$ be a compact Hausdorff space, let $E$ be a Banachspace, and let $C(X,E)$ stand for the Banachspace of $E$-valued continuous functions on $X$ under the uniform norm. In this paper we characterize Integral operators (in the sense of Grothendieck) on $C(X,E)$ spaces in term of their representing vector measures. This is then used to give some applications to Nuclear operators on $C(X,E)$ spaces.

We record a history of the thirteen conferences on Banach algebras that havetaken place; the first was in Los Angeles in 1974 and the thirteenth is the conference inBlaubeuren recorded in the present volume.1991 Mathematics Subject Classification: 46H99, 01A65.PreliminariesThis article is written to record --- at least from the memories of some of theparticipants --- the history of the sequence of conferences on Banach algebras;the Blaubeuren conference is the 13thconference in this sequence. We seek torecord some mathematical and some organizational facts, and to ruminate on thechanging mathematical and organizational scene.In writing this account I have come to realize that my memory is a littlewobblier than I had supposed; even if one was present at an event, one cannotnecessarily recall accurately all the details. One is led to wonder how reliable is thereport of historians, who were not present at the events that they describe. To someextent I have been able t...

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

In this article we introduce and investigate a new class of rearrangement invariant (r.i.) Banach function spaces, so-called Composed Grand Lebesgue Spaces (CGLS), in particular, Integral Grand Lebesgue Spaces (IGLS), which are some generalizations of known Grand Lebesgue Spaces (GLS). We consider the fundamental functions of CGLS, calculate its Boyd's indices, obtain the norm boundedness some (regular and singular) operators in this spaces, investigate the conjugate and associate spaces, show that CGLS obeys the absolute continuous norm property etc.

In this article we extend the notion of quasi-nilpotent equivalent operators, introduced by Colojoara and Foias \\cite{co1} for Banachspaces, to the class of bounded operators on sequentially complete locally convex spaces.

The main result says that every surjective isometry between two ideal Banach function spaces satisfying certain conditions can be presented as a composition of a measurable transformation of a variable and multiplication by a function.

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

The famous Banach-Tarski paradox claims that the three dimensional rotation group acts on the two dimensional sphere paradoxically. In this paper, we generalize their result to show that the classical group acts on the flag manifold paradoxically.

We give a general condition for infinite dimensional unital Abelian Banach algebras to fail the fixed point property. Examples of those algebras are given including the algebras of continuous functions on compact sets.

Full Text Available We give a general condition for infinite dimensional unital Abelian Banach algebras to fail the fixed point property. Examples of those algebras are given including the algebras of continuous functions on compact sets.

In this paper, we show that the essentiality of the scole of an ideal B of the semi-simple Banach algebra A implies that any invertibility preserving isomorphism on A is a Jordan homomorphism. Specially ...

A surjective bounded homomorphism fails to preserve $n$-weak amenability, in general. We however show that it preserves the property if the involved homomorphism enjoys a right inverse. We examine this fact for certain homomorphisms on several Banach algebras.

We give a sufficient criterion for complex analyticity of nonlinear maps defined on direct limits of normed spaces. This tool is then used to construct new classes of (real and complex) infinite dimensional Lie groups: (a) groups of germs of analytic diffeomorphisms around a compact set in a Banachspace and (b) unions of ascending sequences of Banach Lie groups.

[en] A family of infinite-dimensional Grassmann-Banach algebras over a complete normed field K is considered. It is shown that every element G of the family is an associative supercommutative Banach superalgebra over K: G double-bond G0 circle-plus G1 with zero annihilators G0perpendicular double-bond G1perpendicular double-bond(G1(?))perpendicular double-bond(0), k ? 2

Full Text Available Given a Banach algebra A, the compactum of A is defined to be the set of elements xÃ¢ÂˆÂˆA such that the operator aÃ¢Â†Â’xax is compact. General properties of the compactum and its relation to the socle of A are discussed. Characterizations of finite dimensionality of a semi-simple Banach algebra are given in terms of the compactum and the socle of A.

Full Text Available We consider Wiener type algebras on an open Banach ball. In particular, we prove that such algebras consist of functions analytic in this ball. We also consider a property of one-parameter groups generated by an isometric group acting on a Banach ball. We establish that the subspace of exponential type vectors of its generators form a dense subalgebra in a Wiener algebra and a generator is a derivation on this subspace.

Nonlinear higher order difference equations with linear arguments (containing linear forms within nonlinear maps of the space) are well-defined on Banach algebras. The scalar forms of these equations (i.e., with real variables and parameters) have appeared frequently in the literature. By generalizing existing results from real numbers to algebras and using a new result on reduction of order, new sufficient conditions are obtained for the convergence to zero of all solutions of nonlinear difference equations with linear arguments. Where reduction of order is possible, these conditions extend the ranges of parameters for which the origin is a global attractor even when all variables and parameters are real numbers.

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

This is the first part of the second revised and extended edition of a well established monograph. It is an introduction to function spaces defined in terms of differentiability and integrability classes. It provides a catalogue of various spaces and benefits as a handbook for those who use function spaces to study other topics such as partial differential equations. Volume 1 deals with Banach function spaces, Volume 2 with Sobolev-type spaces.

The purpose of this article is to prove existence of mass minimizing integral currents with prescribed possibly non-compact boundary in all dual Banachspaces and furthermore in certain spaces without linear structure, such as injective metric spaces and Hadamard spaces. We furthermore prove a weak$^*$-compactness theorem for integral currents in dual spaces of separable Banachspaces. Our theorems generalize results of Ambrosio-Kirchheim, Lang, the author, and recent results of Ambrosio-Schmidt.

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

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

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

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

The plantar grasp reflex is of great clinical significance, especially in terms of the detection of spasticity. The palmar grasp reflex also has diagnostic significance. This grasp reflex of the hands and feet is mediated by a spinal reflex mechanism, which appears to be under the regulatory control...

In recent experiments at the Harry Diamond Laboratories and at the Naval Research Laboratory, intense microwave emission has been observed during reflex triode operation. A fully relativistic, time-dependent one-dimensional simulation code, based on the technique formulated by Birdsall and Bridges, was written to investigate the collective electron oscillations and to predict the microwave energy spectral density. Predicted and measured reflex triode microwave energy spectral densities in the X-band region are in reasonable agreement with one another and confirm the validity of the model. Computer experiments indicate that microwave generation could be greatly enhanced by feeding the radiated energy back into the oscillating space-charge cloud

Let A be a commutative unital Banach algebra with infinite spectrum. Then by Helemski?'s global dimension theorem the global homological dimension of A is strictly greater than one. This estimate has no analogue for abstract algebras or non-normable topological algebras. It is proved in the present paper that for every unital Banach algebra B the global homological dimensions and the homological bidimensions of the Banach algebras A\\mathbin{\\widehat{\\otimes}}B and B (assuming certain restrictions on A) are related by \\operatorname{dg}A\\mathbin{\\widehat{\\otimes}}B\\geqslant 2+\\operatorname{dg}B and \\operatorname{db}A\\mathbin{\\widehat{\\otimes}}B\\geqslant 2+\\operatorname{db}B. Thus, a partial extension of Helemski?'s theorem to tensor products is obtained. Bibliography: 28 titles.

[en] Let A be a commutative unital Banach algebra with infinite spectrum. Then by Helemskii's global dimension theorem the global homological dimension of A is strictly greater than one. This estimate has no analogue for abstract algebras or non-normable topological algebras. It is proved in the present paper that for every unital Banach algebra B the global homological dimensions and the homological bidimensions of the Banach algebras A widehat-otimes B and B (assuming certain restrictions on A) are related by A widehat-otimes B?2 + dg B and A widehat-otimes B?2 + db B. Thus, a partial extension of Helemskii's theorem to tensor products is obtained. Bibliography: 28 titles.

The paper presents basic concepts of the discrete signalstheory from the viewpoint of Banach algebras and showsthat some Banach algebras of sequences are not only suitablemathematical framework for the multidimensional discretesignals theory but also open ways to new models ofdiscrete systems and lead to hitherto unknown methods ofhomomorphic signal processing and deconvolution.Three Banach algebras of multidimensional sequences areinvestigated in detail with emphasis on the existence ofthe logarithm and invertibility: the algebra of absolutelysummable sequences over an arbitrary semigroup S ae Zn;the algebra of periodic sequencies, and the algebra of sequenceswith finite support. A general formula for theGelfand transform is derived and shown to be a generalizationof the traditional Fourier transforms. Two basic operationsof homomorphic signal processing, cepstrum andinverse cepstrum are shown to be equivalent to the logarithmicand exponential functions; their co...

Our current understanding of brainstem reflex physiology comes chiefly from the classic anatomical-functional correlation studies that traced the central circuits underlying brainstem reflexes and establishing reflex abnormalities as markers for specific areas of lesion. These studies nevertheless had the disadvantage of deriving from post-mortem findings in only a few patients. We developed a voxel-based model of the human brainstem designed to import and normalize MRIs, select groups of patients with or without a given dysfunction, compare their MRIs statistically, and construct three-plane maps showing the statistical probability of lesion. Using this method, we studied 180 patients with focal brainstem infarction. All subjects underwent a dedicated MRI study of the brainstem and the whole series of brainstem tests currently used in clinical neurophysiology: early (R1) and late (R2) blink reflex, early (SP1) and late (SP2) masseter inhibitory reflex, and the jaw jerk to chin tapping. Significance levels were highest for R1, SP1 and R2 afferent abnormalities. Patients with abnormalities in all three reflexes had lesions involving the primary sensory neurons in the ventral pons, before the afferents directed to the respective reflex circuits diverge. Patients with an isolated abnormality of R1 and SP1 responses had lesions that involved the ipsilateral dorsal pons, near the fourth ventricle floor, and lay close to each other. The area with the highest probabilities of lesion for the R2-afferent abnormality was in the ipsilateral dorsal-lateral medulla at the inferior olive level. SP2 abnormalities reached a low level of significance, in the same region as R2. Only few patients had a crossed-type abnormality of SP1, SP2 or R2; that of SP1 reached significance in the median pontine tegmentum rostral to the main trigeminal nucleus. Although abnormal in 38 patients, the jaw jerk appeared to have no cluster location. Because our voxel-based model quantitatively compares lesions in patients with or without a given reflex abnormality, it minimizes the risk that the significant areas depict vascular territories rather than common spots within the territory housing the reflex circuit. By analysing statistical data for a large cohort of patients, it also identifies the most frequent lesion location for each response. The finding of multireflex abnormalities reflects damage of the primary afferent neurons; hence it provides no evidence of an intra-axial lesion. The jaw jerk, perhaps the brainstem reflex most widely used in clinical neurophysiology, had no apparent topodiagnostic value, probably because it depends strongly on peripheral variables, including dental occlusion. PMID:15601661

Cruccu, G; Iannetti, G D; Marx, J J; Thoemke, F; Truini, A; Fitzek, S; Galeotti, F; Urban, P P; Romaniello, A; Stoeter, P; Manfredi, M; Hopf, H C

The vestibulo-ocular reflex (VOR) ensures best vision during head motion by moving the eyes contrary to the head to stabilize the line of sight in space. The VOR has three main components: the peripheral sensory apparatus (a set of motion sensors: the semicircular canals, SCCs, and the otolith organs), a central processing mechanism, and the motor output (the eye muscles). The SCCs sense angular acceleration to detect head rotation; the otolith organs sense linear acceleration to detect both head translation and the position of the head relative to gravity. The SCCs are arranged in a push-pull configuration with two coplanar canals on each side (like the left and right horizontal canals) working together. During angular head movements, if one part is excited the other is inhibited and vice versa. While the head is at rest, the primary vestibular afferents have a tonic discharge which is exactly balanced between corresponding canals. During rotation, the head velocity corresponds to the difference in the firing rate between SCC pairs. Knowledge of the geometrical arrangement of the SCCs within the head and of the functional properties of the otolith organs allows to localize and interpret certain patterns of nystagmus and ocular misalignment. This is based on the experimental observation that stimulation of a single SCC leads v ia the VOR to slowphase eye movements that rotate the globe in a plane parallel to that of the stimulated canal. Furthermore, knowledge of the mechanisms that underlie compensation for vestibular disorders is essential for correctly diagnosing and effectively managing patients with vestibular disturbances.

We study the spectral synthesis for the Banach *-algebra $A\\oop B$, the operator space projective tensor product of $C^*$-algebras $A$ and $B$. It is shown that if $A$ or $B$ has finitely many closed ideals, then $A\\oop B$ obeys spectral synthesis. The Banach algebra $A \\oop A$ with the reverse involution is also studied.

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.

Let $G$ be a locally compact group and also let $H$ be a compact subgroup of $G$. It is shown that, if $\\mu$ is a relatively invariant measure on $G/H$ then there is a well-defined convolution on $L^1(G/H,\\mu)$ such that the Banachspace $L^1(G/H,\\mu)$ becomes a Banach algebra. We also find a generalized definition of this convolution for other $L^p$-spaces. Finally, we show that various types of involutions can be considered on $G/H$.

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

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.

Starlike bodies are interesting in nonlinear analysis because they are strongly related to polynomials and smooth bump functions, and their topological and geometrical properties are therefore worth studying. In this note we consider the question as to what extent the known results on topological cl...

We investigate the stability problem for the following functional inequality ??f((x+y)/2?)+?f((y+z)/2?)+?f((z+x)/2?)???f(x+y+z)? on restricted domains of Banach modules over a C?-algebra. As an application we study t...

Let $S$ be the set of those $\\alpha\\in\\omega_2$ that have cofinality $\\omega_1$. It is consistent relative to a measurable that player II (the nonempty player) wins the pressing down game of length $\\omega_1$, but not the Banach Mazur game of length $\\omega+1$ (both starting with $S$).

In this paper, the notion of spatial numerical range of elements of Banach algebras without identity is studied. Specifically, the relationship between spatial numerical ranges, numerical ranges and spectra is investigated. Among other results, it is shown that the closure of the spatial numerical r...

In this paper, an existence theorem for a certain hyperbolic differential inclusions in Banach algebras is proved under the mixed Lipschitz and Carathéodory conditions. The existence of extremal solutions for Carathéodory as well as discontinuous hyperbolic differential inclusions is also proved under certain monotonicity conditions.

Using an appropriate definition of the multiplicity of a spectral value, we introduce a new definition of the trace and determinant of elements with finite spectrum in Jordan-Banach algebras. We first extend a result obtained by J. Zemánek in the associative case, on the connectedness of projections...

We present two new forms in which the Frechet differential of a power series in a unitary Banach algebra can be expressed in terms of absolutely convergent series involving the commutant $C(T) : A \\rightarrow [A,T]$. Then we apply the results to study series of vector-valued functions on...

Heart rate, blood pressure, and vascular tone, as well as ventilator drive, respiratory rate, and breathing pattern, are, at least in part, under the control of specific reflexes. These reflexes are mediated by a complex network of baroreceptors and chemoreceptors in the arterial system of the carotids, aorta, and left heart, including receptors in the left atrium, the ventricle, and the coronary arteries; irritants in the upper airways and stretch receptors in the lower airways; juxtacapillary-located nonmyelinated fibers in the alveoli and in the bronchial arterial system; and muscle spindles that evoke changes in the membrane potential upon alteration of sarcolemmal tension. Some of these reflexes, usually named after the first individual to describe them, have spread as eponyms into propaedeutic education and clinical work. Because these euphonic eponyms are enigmatic to most clinicians today, this article is intended to provide a short overview of these reflexes, including the historical context of their describers. As evidenced by their clinical implications, the eponyms discussed are revealed to be more than curiosities taught during undergraduate medical education.

If X is a compact Hausdorff space, supplied with a homeomorphism, then a crossed product involutive Banach algebra is naturally associated with these data. If X consists of one point, then this algebra is the group algebra of the integers. In this paper, we study spectral synthesis for the closed ideals of this associated algebra in two versions, one modeled after C(X), and one modeled after the group algebra of the integers. We identify the closed ideals which are equal to (what is the analogue of) the kernel of their hull, and determine when this holds for all closed ideals, i.e., when spectral synthesis holds. In both models, this is the case precisely when the homeomorphism has no periodic points.

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

Full Text Available This paper responds to Jaegwon Kim's powerful objection to the very possibility of genuinely novel emergent properties Kim argue that the incoherence of reflexive downward causation means that the causal power of an emergent phenomenon is ultimately reducible to the causal powers of its constituents. I offer a a simple argument showing how to characterize emergent properties m terms of the effects of structural relations an the causal powers of that constituents.

Bonet, Frerick, Peris and Wengenroth constructed a hypercyclic operator on the locally convex direct sum of countably many copies of the Banachspace $\\ell_1$. We extend this result. In particular, we show that there is a hypercyclic operator on the locally convex direct sum of a sequence $\\{X_n\\}_{n\\in\\N}$ of Fr\\'echet spaces if and only if each $X_n$ is separable and there are infinitely many $n\\in\\N$ for which $X_n$ is infinite dimensional. Moreover, we characterize inductive limits of sequences of separable Banachspaces which support a hypercyclic operator.

In this supplement to [GJ1], [GJ3], we give an intrinsic characterization of (bounded, linear) operators on Banach lattices which factor through Banach lattices not containing a copy of $c_0$ which complements the characterization of [GJ1], [GJ3] that an operator admits such a factorization if and only if it can be written as the product of two operators neither of which preserves a copy of $c_0$. The intrinsic characterization is that the restriction of the second adjoint of the operator to the ideal generated by the lattice in its bidual does not preserve a copy of $c_0$. This property of an operator was introduced by C. Niculescu [N2] under the name ``strong type B".

Ghoussoub, N; Ghoussoub, Nassif; Johnson, William B.

Let $\\Omega$ be a compact Hausdorff space, let $E$ be a Banachspace, and let $C(\\Omega, E)$ stand for the Banachspace of all $E$-valued continuous functions on $\\Omega$ under supnorm. In this paper we study when nuclear operators on $C(\\Omega, E)$ spaces can be completely characterized in terms of properties of their representing vector measures. We also show that if $F$ is a Banachspace and if $T:\\ C(\\Omega, E)\\rightarrow F$ is a nuclear operator, then $T$ induces a bounded linear operator $T^\\#$ from the space $C(\\Omega)$ of scalar valued continuous functions on $\\Omega$ into $\\slN(E,F)$ the space of nuclear operators from $E$ to $F$, in this case we show that $E^*$ has the Radon-Nikodym property if and only if $T^\\#$ is nuclear whenever $T$ is nuclear.

We present results on local solubility, extendability of solutions, and the existence of upper and lower solutions of equations with monotonic generalized Volterra operators in Banach function spaces. These results are analogous to the well-known theorems on the integral and differential inequality and can be used for estimating solutions of various functional-differential equations.

Reflexive functors of modules are ubiquitous in Algebraic Geometry, mainly in the theory of linear representations of group schemes, and in "duality theories". In this paper we study and determine reflexive functors and we give many properties of reflexive functors.

Reflex sympathetic dystrophy, causalgia, Sudeck's atrophy, shoulder-hand syndrome, and transient osteoporosis represent a spectrum of sympathetic disturbances which typically present with regional findings. They are often pauciarticular in distribution and uniquely sensitive to timely therapeutic intervention and to preventative measures. Clinical and radiologic appearances are quite characteristic. Thermographic examination provides a valuable tool for monitoring the therapeutic response. The major factor in therapeutic efficacy is aggressive physical therapy. Although therapeusis has been facilitated by a multitude of agents, therapeutic resistance is unfortunately the circumstance, when intervention is delayed.

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.

In this paper we study the relationships among the spectra of the cosets of an element of a Banach algebra in some quotient algebras. We also characterize the spectrum of any aÃ¢ÂˆÂˆM (where M is an ideal of a Banach algebra with identity and moreover has an identity) in the whole algebra in terms o...

Full Text Available Let (?, A, ?) is a finite measure space, E an order continuous Banach function space over ?, X a Banachspace 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*.

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

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 Banachspace or Hilbert space, we reduced the completeness and the uniform convexity assumptions which imposed on the given normed space.

Let $E$ and $F$ be Banach lattices. Let $G$ be a vector sublattice of $E$ and $T: G\\rightarrow F$ be an order continuous positive compact (resp. weakly compact) operators. We show that if $G$ is an ideal or an order dense sublattice of $E$, then $T$ has a norm preserving compact (resp. weakly compact) positive extension to $E$ which is likewise order continuous on $E$. In particular, we prove that every compact positive orthomorphism on an order dense sublattice of $E$ extends uniquely to a compact positive orthomorphism on $E$.

Full Text Available Generalizations of Banach's fixed point theorem are proved for a large class of non-metric spaces. These include d-complete symmetric (semi-metric) spaces and complete quasi-metric spaces. The distance function used need not be symmetric and need not satisfy the triangular inequality.

In this paper we prove an isoperimetric inequality of euclidean type for complete metric spaces admitting a cone-type inequality. These include all Banachspaces and all complete, simply-connected metric spaces of non-positive curvature in the sense of Alexandrov or, more generally, of Busemann. The main theorem generalizes results of Gromov and Ambrosio-Kirchheim.

Full Text Available The aim of the present article is to give some general methods inthe fixed point theory for mappings of general topological spaces. Using the notions of the multi-metric space and of the E-metric space, we proved the analogous of several classical theorems: Banach fixed point principle, Theorems of Edelstein, Meyers, Janos etc.

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.

We study the (non-uniform) quantified constraint satisfaction problem QCSP(H) as H ranges over partially reflexive forests. We obtain a complexity-theoretic dichotomy: QCSP(H) is either in NL or is NP-hard. The separating condition is related firstly to connectivity, and thereafter to accessibility from all vertices of H to connected reflexive subgraphs. In the case of partially reflexive paths, we give a refinement of our dichotomy: QCSP(H) is either in NL or is Pspace-complete.

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.

The reasoning that neural reflexes maintain homeostasis in other body organs, and that the immune system is innervated, prompted a search for neural circuits that regulate innate and adaptive immunity. This elucidated the inflammatory reflex, a prototypical reflex circuit that maintains immunological homeostasis. Molecular products of infection or injury activate sensory neurons traveling to the brainstem in the vagus nerve. The arrival of these incoming signals generates action potentials that travel from the brainstem to the spleen and other organs. This culminates in T cell release of acetylcholine, which interacts with ?7 nicotinic acetylcholine receptors (?7 nAChR) on immunocompetent cells to inhibit cytokine release in macrophages. Herein is reviewed the neurophysiological basis of reflexes that provide stability to the immune system, the neural- and receptor-dependent mechanisms, and the potential opportunities for developing novel therapeutic devices and drugs that target neural pathways to treat inflammatory diseases.

Starting with a complex commutative semi-simple regular Banach algebra $A$ and an automorphism $\\sigma$ of $A$, we form the crossed product of $A$ with the integers, where the latter act on $A$ via iterations of $\\sigma$. The automorphism induces a topological dynamical system on the character space $\\Delta(A)$ of $A$ in a natural way. We prove an equivalence between the property that every non-zero ideal in the crossed product has non-zero intersection with the subalgebra $A$, maximal commutativity of $A$ in the crossed product, and density of the non-periodic points of the induced system on the character space. We also prove that every non-trivial ideal in the crossed product always intersects the commutant of $A$ non-trivially. Furthermore, under the assumption that $A$ is unital and such that $\\Delta(A)$ consists of infinitely many points, we show equivalence between simplicity of the crossed product and minimality of the induced system, and between primeness of the crossed product and topological transitivity of the system.

Steady-state space charge limited-flow calculations have been carried out for an applied B/sub theta/ magnetically insulated reflexing ion diode. Reflex ion energy spectra characteristic of a thin foil cathode and of a transparent mesh have been used. A one-dimensional calculation shows higher ion current densities with a mesh cathode, and that the emission electron current density increases with the applied B/sub theta/ magnetic field. The ion current density is calculated to increase slightly with radius.

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 during the crank cycle, producing ankle dorsiflexion perturbations of similar trajectory. The stretch reflex was greatest during the power phase of the crank cycle and was decreased to the level of background EMG during recovery. Matched perturbations were induced under static conditions at the same crank angle and background soleus EMG as recorded during the power phase of active pedaling. The magnitude of the stretch reflex was not statistically different from that during the static condition throughout the power phase of the movement. The results of this study indicate that the stretch reflex is not 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.

Reflex Sympathetic Dystrophy is rare in pediatrics. It is a complex regional pain syndrome, of unknown etiology, usually post-traumatic, characterized by dysfunctions of the musculoskeletal, vascular and skin systems: severe persistent pain of a limb, sensory and vascular alterations, associated disability and psychosocial dysfunction. The diagnosis is based in high clinical suspection. In children and adolescents there are aspects that are different from the adult ones. Excessive tests may result in worsening of the clinical symptoms. Bone scintigraphy can help. Pain treatment is difficult, not specific. Physical therapies and relaxation technics give some relief. Depression must be treated. This syndrome includes fibromyalgia and complex regional pain syndrome type I. We present a clinical report of an adolescent girl, referred for pain, cold temperature, pallor and functional disability of an inferior limb, all signals disclosed by a minor trauma. She had been diagnosed depression the year before. The bone scintigraphy was a decisive test. The treatment with gabapentin, C vitamin, physiotherapy and pshycotherapy has been effective. PMID:22713207

Full Text Available There are some papers, such as [1], [2] and [3], in which some properties on isomorphism of closed subspace lattices of Hilbert spaces were studied. In this short paper we will point out that the hyper-reflexivity of closed subspace lattice is invariant under isomorphism of ÃŽÂ¾(H1) on ÃŽÂ¾(H2). We also proved that if T is in L(H) such that 0Ã¢ÂˆÂˆÃ‚Â¯ÃÂ€(T) and Ã¢Â„Â± is a hyper-reflexive subspace lattice, then ÃÂ•T(Ã¢Â„Â±)Ã¢ÂˆÂª{H} is hyper-reflexive where ÃÂ•T is a homomorphism induced by T.

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.

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.

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.

Amr Abdulazim; Ashkan Rashad; Behnam Bohluli; Bernhard Schaller; Fatemeh Momen-Heravi; Pooyan Sadr-Eshkevari

We characterize the projectors $ P $ on a Banachspace $ E $ with the property of being connected to all the others projectors obtained as a conjugation of $ P $. Such property is described in in terms of the general linear group of the spaces $ \\mathrm{Range} .1em $, $ \\mathrm{Ker} >.1em $ and $ E $. Using this characterization we obtain the well known facts that finite-dimensional and finite-co-dimensional projectors lie in the same connected component of their conjugates. Finally we exhibit an example of Banachspace where the conjugacy class of a projector splits into several arcwise components. Such example was first obtained by G. Porta and L. Recht (Acta Cientifica Venezolana, 1987) for the Banach algebra of continuous 2x2 complex matrices-valued functions on $ S^3 $. Thus we show that counterexamples also exists among the algebras of bounded operators.

Full Text Available We propose another extension of Orlicz-Sobolev spaces to metric spaces based on the concepts of the ÃŽÂ¦-modulus and ÃŽÂ¦-capacity. The resulting space NÃŽÂ¦1 is a Banachspace. The relationship between NÃŽÂ¦1 and MÃŽÂ¦1 (the first extension defined in AÃƒÂ¯ssaoui (2002)) is studied. We also explore and compare different definitions of capacities and give a criterion under which NÃŽÂ¦1 is strictly smaller than the Orlicz space LÃŽÂ¦.

Full Text Available In this paper we study the relationships among the spectra of the cosets of an element of a Banach algebra in some quotient algebras. We also characterize the spectrum of any aÃ¢ÂˆÂˆM (where M is an ideal of a Banach algebra with identity and moreover has an identity) in the whole algebra in terms of the spectrum of a in M.

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

Let $A$ be a Banach algebra. By $\\sigma(x)$ and $r(x)$ we denote the spectrum and the spectral radius of $x\\in A$, respectively. We consider the relationship between elements $a,b\\in A$ that satisfy one of the following two conditions: (1) $\\sigma(ax) = \\sigma(bx)$ for all $x\\in A$, (2) $r(ax) \\le r(bx)$ for all $x\\in A$. In particular we show that (1) implies $a=b$ if $A$ is a $C^*$-algebra, and (2) implies $a\\in \\mathbb C b$ if $A$ is a prime $C^*$-algebra. As an application of the results concerning the conditions (1) and (2) we obtain some spectral characterizations of multiplicative maps.

Full Text Available To discuss reflexivity in anthropology is not a new approach. The purpose of this article is to examine the meaning of reflexivity for the hermeneutical or confessional anthropology, which has been endemic in social sciences ever since the publication of Malinowski’s di- aries and the onset of the recurrent and persistent crisis of objectivity that haunts modern scholarship. We have determined that anthropology is no longer a one-sided, self-centred, objective science. Today anthropology is interpreted for its subjectivity and its multiple faces that create a mosaic reflection of the anthropologist and the researcher. This article aims not to be innovative, for it is far from accomplishing such a task. This article, howe- ver, discusses the coherence of a discourse that emanates from contested narratives about the self. It responds to what some call the reflexive turn in anthropology – a homology between defamiliarisation and literary exposition, which undermines the fictionality (or the falsehood) of anthropological writing, in the sense that each reflexive critique is in its own right an autonomous interpretation, blurring the lines between the true and the imaginary (understood from Latin as a sort of plastic modelling, self-construction). Reflexivity is all: a turn into the deeper self, which denudes, and a hypothesis into the construction of meaning.

Reflex seizures are a rare phenomenon among epileptic patients, in which an epileptic discharge is triggered by various kinds of stimuli (visual, auditory, tactile or gustatory). Epilepsy is common in Rett syndrome patients (up to 70%), but to the authors' knowledge, no pressure or eating-triggered seizures have yet been reported in Rett children. We describe three epileptic Rett patients with reflex seizures, triggered by food intake or proprioception. One patient with congenital Rett Sd. developed infantile epileptic spasms at around seven months and two patients with classic Rett Sd. presented with generalised tonic-clonic seizures at around five years. Reflex seizures appeared when the patients were teenagers. The congenital-Rett patient presented eating-triggered seizures at the beginning of almost every meal, demonstrated by EEG recording. Both classic Rett patients showed self-provoked pressure -triggered attacks, influenced by stress or excitement. Non-triggered seizures were controlled with carbamazepine or valproate, but reflex seizures did not respond to antiepileptic drugs. Risperidone partially improved self-provoked seizures. When reflex seizures are suspected, reproducing the trigger during EEG recording is fundamental; however, self-provoked seizures depend largely on the patient's will. Optimal therapy (though not always possible) consists of avoiding the trigger. Stress modifiers such as risperidone may help control self-provoked seizures.

Roche Martínez A; Alonso Colmenero MI; Gomes Pereira A; Sanmartí Vilaplana FX; Armstrong Morón J; Pineda Marfa M

In this paper we give a characterization of atomic decompositions, Banach frames, $X_d$-Riesz bases, $X_d$-frames, $X_d$-Bessel sequences, sequences satisfying the lower $X_d$-frame condition, duals of $X_d$-frames and synthesis pseudo-duals, based on an operator acting on the canonical basis of a sequence space. We discuss expansions in $X$ and $X^*$. Further, we consider necessary and sufficient conditions on operators to preserve the sequence type of the listed concepts. As a consequence, we solve some problems in Hilbert frame theory.

We establish H\\"older type inequalities for Lorentz sequence spaces and their duals. In order to achieve these and some related inequalities, we study diagonal multilinear forms in general sequence spaces, and obtain estimates for their norms. We also consider norms of multilinear forms in different Banach multilinear ideals.

In this paper, first we have established two sets of sufficient conditions for a mapping to have unique fixed point in a intuitionistic fuzzy metric space and then we have redefined the contraction mapping in a intuitionistic fuzzy metric space and thereafter we proved the Banach Fixed Point theorem.

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).

Full Text Available The concept of a reflexive algebra (ÃÂƒ-algebra) ÃŽÂ² of subsets of a set X is defined in this paper. Various characterizations are given for an algebra (ÃÂƒ-algebra) ÃŽÂ² to be reflexive. If V is a real vector lattice of functions on a set X which is closed for pointwise limits of functions and if ÃŽÂ²={A|AÃ¢Â«Â…XÃ¢Â€Â‰Ã¢Â€Â‰Ã¢Â€Â‰andÃ¢Â€Â‰Ã¢Â€Â‰Ã¢Â€Â‰CA(x)Ã¢ÂˆÂˆV} is the ÃÂƒ-algebra induced by V then necessary and sufficient conditions are given for ÃŽÂ² to be reflexive (where CA(x) is the indicator function).

In this paper we describe the L-characteristic of the nonlinear superposition operator F(x) f(s,x(s)) between two Banachspaces 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 ?-convexity property. In this paper we show that L-characteristic of the operator F (between two Banachspaces) 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 Banachspaces 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.

We prove a transference principle for general (i.e., not necessarily bounded) strongly continuous groups on Banachspaces. If the Banachspace has the UMD property, the transference principle leads to estimates for the functional calculus of the group generator. In the Hilbert space case, the results cover classical theorems of McIntosh and Boyadzhiev-de Laubenfels; in the UMD case they are analogues of classical results by Hieber and Pruess. By using functional calculus methods, consequences for sectorial operators are derived. For instance it is proved, that every generator of a cosine function on a UMD space has bounded H-infinity calculus on sectors.

A topological space $X$ is called $\\Cal A$-real compact, if every algebra homomorphism from $\\Cal A$ to the reals is an evaluation at some point of $X$, where $\\Cal A$ is an algebra of continuous functions. Our main interest lies on algebras of smooth functions. In \\cite{AdR} it was shown that any separable Banachspace is smoothly real compact. Here we generalize this result to a huge class of locally convex spaces including arbitrary products of separable Fr\\'echet spaces.

Full Text Available We prove the Hyers-Ulam-Rassias stability of homomorphisms in real Banach algebras and of generalized derivations on real Banach algebras for the following Cauchy-Jensen functional equations: , , which were introduced and investigated by Baak (2006). The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias' stability theorem that appeared in his paper (1978).

In this survey, at first we review to many examples which have been made on cone metric spaces to verify some properties of cones on real Banachspaces and cone metrics and second, in continue like as examples that sandwich theorem doesn't hold and we shall present an other example that comparison test doesn't hold with an example for normal cones.

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.

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 and iterated in light of research questions.

Full Text Available Two issues are explored in this article: the way in which "space" has been theorized in relation to the "sacred", and the use of contemporary cultural and social theories of space in the development of a methodology for locating religion in places, objects, bodies and groups open to investigation. After a brief recollection of the spatial contributions of van der Leeuw and Eliade, attention is given to the theoretical and methodological insights of Jonathan Z. Smith, Veikko Anttonen, and Kim Knott.

In this article, we define a natural Banach *-algebra for a C*-dynamical system (A,G,[alpha]) which is slightly bigger than L1(G;A) (they are the same if A is finite-dimensional). We will show that this algebra is *-regular if G has polynomial growth. The main result in this article extends the two main results in [C.W. Leung, C.K. Ng, Functional calculus and *-regularity of a class of Banach algebras, Proc. Amer. Math. Soc., in press].

Several features of an analytic (infinite-dimensional) Grassmannian of (commensurable) subspaces of a Hilbert space were developed in the context of integrable PDEs (KP hierarchy). We extended some of those features when polarized separable Hilbert spaces are generalized to a class of polarized Hilbert modules, in particular the Baker and tau-functions, which become operator-valued. Following from Part I we produce a pre-determinant structure for a class of tau-functions defined in the setting of the similarity class of projections of a certain Banach *-algebra. This structure is explicitly derived from the transition map of a corresponding principal bundle. The determinant of this map gives a generalized, operator-valued tau-function that takes values in a commutative C*-algebra. We extend to this setting the operator cross-ratio which had been used to produce the scalar-valued tau-function, as well as the associated notion of a Schwarzian derivative along curves inside the space of similarity classes. We li...

Full Text Available Abstract As a generalization to Banach contraction principle, ?iri? introduced the concept of quasi-contraction mappings. In this paper, we investigate these kinds of mappings in modular function spaces without the -condition. In particular, we prove the existence of fixed points and discuss their uniqueness.

The comparison type version of the fixed point result in ordered metric spaces established by Nieto and Rodriguez-Lopez [Acta Math. Sinica (English Series), 23 (2007), 2205-2212] is nothing but a particular case of the classical Banach's contraction principle [Fund. Math., 3 (1922), 133-181].

A Wiener-Hopf operator on a Banachspace of functions on R+ is a bounded operator T such that P^+S_{-a}TS_a=T, for every positive a, where S_a is the operator of translation by a. We obtain a representation theorem for the Wiener-Hopf operators on a large class of functions on R+ with values in a separable Hilbert space.

The asymptotic behaviour of unbounded trajectories for non expansive mappings in a real Hilbert space and the extension to more general Banachspaces and to nonlinear contraction semi-group have been studied by many authors. In this paper we study the asymptotic behaviour of unbounded trajectories for a quasi non-autonomous dissipative systems. 26 refs.

We investigate a class of non-linear partial differential equations with discrete state-dependent delays. The existence and uniqueness of strong solutions for initial functions from a Banachspace are proved. To get the well-posed initial value problem we restrict our study to a smaller metric space, construct the dynamical system and prove the existence of a compact global attractor.

What. This chapter concerns how visual methods and visual materials can support visually oriented, collaborative and creative learning processes in education. The focus is on facilitation (guiding, teaching) with visual methods in learning processes that are designerly, or that involve design. Visual methods are exemplified through two university classroom cases about collaborative idea generation processes. The visual methods and materials in the cases are photo elicitation using photo cards, and modeling with LEGO Serious Play sets. Why. The goal is to encourage the reader, whether student or professional, to facilitate with visual methods in a critical, reflective and experimental way. The chapter offers recommendations for facilitating with visual methods to support playful, emergent designerly processes. The chapter also has a critical, situated perspective. Where. This chapter offers case vignettes that refer to design-oriented workshops where student groups generate ideas, such as for a campaign. The cases are set at Roskilde University. How. There are recommendations on how to facilitate workshops and develop your own practice as a reflexive facilitator. Some of the typical facilitation challenges are discussed, including supporting difficult group collaborative processes (such as dealing with interpersonal tensions). The reader gains understanding about how and why to work with visual methods and how to develop a dynamic, reflexive facilitation practice. The chapter contains recommendations on four aspects that can develop facilitation – being attentive to situatedness, differences, challenges and nurturing reflexivity. Theoretical perspectives on facilitating with visual methods are discussed using pragmatic and dialogic approaches. A summary of facilitation stages is presented through a generic model (PASIR).

An asymptotic approximation theory is developed for some classes of linear second-order difference equations in Banach algebras, subject to "finite moments perturbations." The special case of linear matrix difference equations (or, equivalently, of second-order systems) is included. Rigorous and explicitly computable bounds for the error terms are obtained.

Let $R$ be a commutative complex unital semisimple Banach algebra with the involution $\\cdot ^\\star$. Sufficient conditions are given for the existence of a stabilizing solution to the $H^\\infty$ Riccati equation when the matricial data has entries from $R$. Applications to spatially distributed systems are discussed.

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.

Full Text Available Abstract in english Let A , B be two rings. A mapping ? : A ? B is called quartic derivation, if ? is a quartic function satisfies ?(ab) = a4?(b) + ?(a)b4 for all a, b ? A. The main purpose of this paper to prove the generalized Hyers-Ulam-Rassias stability of the quartic derivations on Banach algebras.

Full Text Available Let A , B be two rings. A mapping ? : A ? B is called quartic derivation, if ? is a quartic function satisfies ?(ab) = a4?(b) + ?(a)b4 for all a, b ? A. The main purpose of this paper to prove the generalized Hyers-Ulam-Rassias stability of the quartic derivations on Banach algebras.

This paper concerns a class of Banach valued processes which have finite quadratic variation. The notion introduced here generalizes the classical one, of Métivier and Pellaumail which is quite restrictive. We make use of the notion of $\\chi$-covariation which is a generalized notion of covariation ...

INTRODUCTION: Reflex sympathetic dystrophy (Complex Regional Pain Syndrome type 1) is little known by dermatologists. We report a pediatric case of reflex sympathetic dystrophy with predominant cutaneous involvement. CASE REPORT: A 10 year-old girl presented a warm, painful and relapsing right hand edema for seven months (three outbreaks). The hand was cyanotic, pigmented and painful. Routine blood tests were normal. Radiography and radionuclide bone scan were consistent with stage 1 reflex sympathetic dystrophy. Physiotherapy led to dramatic improvement. DISCUSSION: Reflex sympathetic dystrophy is known since the XVIIIth century. In the last decade, progress in radiology and bone scan have provided elements for understanding the physiopathology of the disease. Microvascular abnormalities under the control of sympathetic nervous system are characteristic of different stages of reflex sympathetic dystrophy. Recently, neurovascular system experiments showed that sympathetic reflex tonus changes may be controlled by the central nervous system. Dermatologic changes of reflex sympathetic dystrophy are well known: edema and erythema in first stage, cyanosis in second stage, sclerosis and atrophia in third stage, but pediatric cases are rarely reported. CONCLUSION: Reflex sympathetic dystrophy is a complex disease, however its physiopathology is now understood. The clinical presentation can be atypical and the dermatologist may be the first to be consulted.

Jouary T; Boralevi F; Pillet P; Taieb A; Léauté-Labrèze C

In 16 patients with spastic paralysis the hamstrings stretch reflex was found to increase as the velocity of stretch increased, and generally to subside after movement ceased. These effects are attributable to the dynamic property of the primary spindle ending. The stretch reflex commonly appeared i...

The reflexive dimension refldim(P) of a lattice polytope P is the minimal d so that P is the face of some d-dimensional reflexive polytope. We show that refldim(P) is finite for every P, and give bounds for refldim(kP) in terms of refldim(P) and k.

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.

Isotope investigation of reflex sympathetic dystrophy is not limited to an evaluation of bony up-take, it also includes examination of the early dynamic scintigraphy of the vessels. The late views of bone scans reflect, above all, the bone's affinity for phosphate complexes i.e. the degree of osteoblast activity. Generally, dystrophies, independent of their site, show increased locoregional uptake, often quite intense, which appears early in the course of the disease. This supports histopathological findings. There are several advantages in using the bone scan in the investigation of reflex dystrophy: early diagnosis before the development of radiological signs, precise evaluation of the local extension of the dystrophic process and detection of the incidence of multifocal forms, follow-up of the course of the disease, definition of new clinical forms: patchy algodystrophy partial, decalcifying dystrophy, sub-radiological dystrophy, the aetiology in certain sites (especially the hip). Early dynamic scans that dystrophy is accompanied by an increase in the vascular compartment and decreased circulatory flow, a sign of the local stage of the disease. There is also an increase of the interstitial compartment, greater than that of the vascular compartment, explaining the presence of edema. The pathophysiological information gained from dynamic studies is matched by the therapeutic information: evaluation, or even prediction, of the effect of a given drug (cortisone, calcitonin).

In France, from january 1, 2000, new LP Gas vehicles equipped by OEM's or vehicles being retro-fitted with LP Gas equipments must be fitted with a R67-01 type safety relief valve. But some 120,000 vehicles, on the roads before January, 1, were left behind without this safety device. Now they can be re-equipped through a programme authorised by a decree of French Authorities. French LP Gas marketers and Public Authorities will cover together 50 % of the costs. A grouping - named 'Operation Reflexe GPL' - was set up by the LP Gas marketers to drive the operation. Thus, at the end of 2001, all LP Gas vehicles in France will be equipped with this safety relief valve, one year ahead of the other European countries. (authors)

[en] The dynamics was numerically studied of electrons and ions in systems with virtual or reflex cathodes by means of 1.5-dimensional PIC simulation model OREBIA-REX in close correlation with the experimental work on relativistic high-current electron beam and ion beam generation. The results of numerical simulation of the formation and relaxation of an oscillating electron beam are discussed. A possible explanation is given of the enhanced energy deposition observed in the REBEX experiment with short plasma columns. Planar reflex diodes and symmetrical reflex triodes, coupled to an external circuit and operated with and without ions, are investigated. In regimes with ions, besides fast oscillations of the diode (triode) voltage and current, slower oscillations due to electron-ion relaxation processes also appear, even leading to periodical collapses of the high-voltage triode. Phase-space diagrams illustrating the motion of particles and time-dependent contour maps of electric field strength and potential are presented. (J.U.)

For $n\\geq 2, p2,$ does there exist an $n$-dimensional Banachspace 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

We prove the Hyers-Ulam-Rassias stability of homomorphisms in real Banach algebras and of generalized derivations on real Banach algebras for the following Cauchy-Jensen functional equations: f(x+y/2+z)+f(xÃ¢ÂˆÂ’y/2+z)=f(x)+2f(z), 2f(x+y/2+z)=f(x)+f(y)+2f(z), which were introduced and investigated b...

Full Text Available Abstract in english An n × n real matrix P is said to be a generalized reflection matrix if P T = P and P² = I (where P T is the transpose of P). A matrix A ? Rn×n is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix P if A = P A P (A = - P A P). The reflexive and anti-reflexive matrices have wide applications in many fields. In this article, two iterative algorithms are proposed to solve the coupled matrix equations { A1 XB1 + C1X T D1 (more) = M1. A2 XB2 + C2X T D2 = M2. over reflexive and anti-reflexive matrices, respectively. We prove that the first (second) algorithm converges to the reflexive (anti-reflexive) solution of the coupled matrix equations for any initial reflexive (anti-reflexive) matrix. Finally two numerical examples are used to illustrate the efficiency of the proposed algorithms. Mathematical subject classification: 15A06, 15A24, 65F15, 65F20.

The examination of Achilles tendon reflex is widely used as a simple, noninvasive clinical test in diagnosis and pharmacological therapy monitoring in such diseases as: hypothyroidism, hyperthyroidism, diabetic neuropathy, the lower limbs obstructive angiopathies and intermittent claudication. Presented Achilles tendon reflect measuring system is based on the piezoresistive sensor connected with the cylinder-piston system. To determinate the moment of Achilles tendon stimulation a detecting circuit was used. The outputs of the measuring system are connected to the PC-based data acquisition board. Experimental results showed that the measurement accuracy and repeatability is good enough for diagnostics and therapy monitoring purposes. A user friendly, easy-to-operate measurement system fulfills all the requirements related to recording, presentation and storing of the patients' reflexograms.

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 (non)engagement 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'.

The authors present their 30 years' experience with expiration reflex. The reflex can be elicited from vocal folds by mechanical, chemical or electrical stimulation of the superior laryngeal nerve of man and laboratory animals, except mice and rats. It manifests itself by a short, forcible expiratory effort without a preceding inspiration which is indispensable for cough effort. The role of expiration reflex is to prevent penetration of foreign bodies into airways, expelling phlegm and detritus from subglottal area. The initial inspiration before expiration is undesired and could lead to inspiration pneumonia. The reflex is well known to laryngologists as '"laryngeal cough." Its receptors are small in number, localised mainly in medial margin of vocal folds deep in mucosa which can explain their stability in pathological conditions of the larygx. Afferentiation of the reflex is via laryngeal nerve similarly to sneezing and cough. Expiration reflex is not co-ordinated by a single "centre" but rather by a network system in the brain stem. Its motor pattern is supposedly produced by "multifunctional" population of medullar neurones in Botzinger complex and the rostral ventral respiratory group involved also in the genesis of breathing and cough. However, in cats also other neurones may play a vital role in production, shaping and mediation of the motor pattern of respiratory reflex, localised in rostral pons, lateral tegmental field or in the raphe medullar midline.

Full Text Available Regular LB-space is fast complete but may not be quasi-complete. Regular inductive limit of a sequence of fast complete, resp. weakly quasi-complete, resp. reflexiveBanach, spaces is fast complete, resp. weakly quasi-complete, resp. reflexive complete, space.

Regular LB-space is fast complete but may not be quasi-complete. Regular inductive limit of a sequence of fast complete, resp. weakly quasi-complete, resp. reflexiveBanach, spaces is fast complete, resp. weakly quasi-complete, resp. reflexive complete, space.

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.

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.

CONTEXT: Irvin M. Korr, PhD, hypothesized that sensitivity of the monosynaptic stretch reflex (ie, deep tendon reflex) plays a major role in the restriction-of-motion characteristic of somatic dysfunction, and that restoration of range of motion through osteopathic manipulative treatment (OMT) could be achieved by resetting of the stretch receptor gain. OBJECTIVE: To test Korr's hypothesis in the context of Achilles tendinitis, examining whether OMT applied to patients with Achilles tendinitis reduces the strength of the stretch reflex. METHODS: Subjects were recruited through public advertisements and referrals from healthcare professionals. There were no recruitment restrictions based on demographic factors. Amplitudes for stretch reflex and H-reflex (Hoffmann reflex) in the triceps surae muscles (the soleus together with the lateral and medial heads of the gastrocnemius) were measured in subjects with diagnosed Achilles tendonitis (n=16), both before and after OMT. These measurements were also made in asymptomatic control subjects (n=15) before and after sham manipulative treatment. RESULTS: As predicated on the concepts of the strain-counterstrain model developed by Lawrence H. Jones, DO, the use of OMT produced a 23.1% decrease in the amplitude of the stretch reflex of the soleus (P<.05) in subjects with Achilles tendinitis. Similarly significant responses were measured in the lateral and medial heads of the gastrocnemius in OMT subjects. The H-reflex was not significantly affected by OMT. In control subjects, neither reflex was significantly affected by sham manipulative treatment. By using a rating scale on questionnaires before treatment and daily for 7 days posttreatment, OMT subjects indicated significant clinical improvement in soreness, stiffness, and swelling. CONCLUSION: The reduction of stretch reflex amplitude with OMT, together with no change in H-reflex amplitude, is consistent with Korr's proprioceptive hypothesis for somatic dysfunction and patient treatment. Because subjects' soreness ratings also declined immediately after treatment, decreased nociceptor activity may play an additional role in somatic dysfunction, perhaps by altering stretch reflex amplitude.

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

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.

The Hoffmann reflex (H-reflex) and direct motor response (M) were investigated (latency, amplitude and excitability curves were analyzed) in patients with senile dementia of the Alzheimer's type (SDAT). M responses had similar latencies in SDAT patients and old control subjects. H reflex latencies were similar in SDAT patients and old control subjects but longer than in younger controls. The H max/M max ratio was also lower in SDAT patients and old control subjects than in younger controls. The excitability curve of the H-reflex (using a double shock procedure) in SDAT patients was lower than in non-demented old controls for all values of the interstimulus intervals.

To investigate the relationship between primitive reflexes and typical early motor development, 156 full-term infants with normal 18-month developmental outcomes were assessed using a modified Primitive Reflex Profile (PRP) and the Alberta Infant Motor Scale (AIMS) at 6 weeks and 3 and 5 months. No significant positive or negative correlations were obtained between the scores of the PRP and the AIMS at any of the ages assessed. Similarly, PRP scores did not differ between infants scoring above and below the 50th percentile on the AIMS. Primitive reflexes were unrelated to motor development. If this finding is maintained among infants at risk for motor disability, observational assessment of spontaneously generated movement, rather than isolated testing of primitive reflexes, might yield more valuable information on the child's overall level of maturation. Intervention for children with identified motor delays or neurological impairments might not need to be focused on either suppression or enhancement of these motor functions.

To investigate the relationship between primitive reflexes and typical early motor development, 156 full-term infants with normal 18-month developmental outcomes were assessed using a modified Primitive Reflex Profile (PRP) and the Alberta Infant Motor Scale (AIMS) at 6 weeks and 3 and 5 months. No significant positive or negative correlations were obtained between the scores of the PRP and the AIMS at any of the ages assessed. Similarly, PRP scores did not differ between infants scoring above and below the 50th percentile on the AIMS. Primitive reflexes were unrelated to motor development. If this finding is maintained among infants at risk for motor disability, observational assessment of spontaneously generated movement, rather than isolated testing of primitive reflexes, might yield more valuable information on the child's overall level of maturation. Intervention for children with identified motor delays or neurological impairments might not need to be focused on either suppression or enhancement of these motor functions. PMID:9213229

Reflexivity is fundamental to qualitative health research, yet notoriously difficult to unpack. Drawing on Wilfred Bion's work on the development of the capacity to think and to learn, I show how the capacity to think is an impermanent and fallible capacity, with the potential to materialize or evaporate at any number of different points. I use this conceptualization together with examples from published interview data to illustrate the difficulties for researchers attempting to sustain a reflexive approach, and to direct attention toward the possibilities for recovering and supporting the capacity to think. I counter some of the criticisms suggesting that reflexivity can be self-indulgent, and suggest instead that self-indulgence constitutes a failure of reflexivity. In the concluding discussions I acknowledge tensions accompanying the use of psychoanalytic theories for research purposes, and point to emerging psychosocial approaches as one way of negotiating these.

Full Text Available This paper attempts to comprehensively concentrate and critically reflect upon the theoretical and methodological conception of sociological reflexivity. It thus concisely presents some relevant debates on reflexivity’s most influential sociological and epistemological definitions, as well as on its varied and complex relationship with the contentious notions of the self and spokespersonship. The conceptual elaboration on both notions emphatically highlights the crucial importance of the relational dimension over against the ubiquitous risks and dangers of subjectivism/objectivism, reification (blackboxing) and essentialism. In addition, it is described and demonstrated the particular significance of the apophatic dimension of reflexivity over against its eurocentric (or western-centric) and over-activistic (or cataphatic) dimension, which inevitably leads to an excessive analytic emphasis upon a highly ordering, instrumental, and chronically monitoring approach to the inherently dynamic and fluid processes of self-awareness, self-experience, self-definition and self-identity.

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(ÃŽ...

A Liouville-Green (WKB) asymptotic approximation theory is developed for some classes of linear second-order difference equations in Banach algebras. The special case of linear matrix difference equations (or, equivalently, of second-order systems) is emphasized. Rigorous and explicitly computable bounds for the error terms are obtained, and this when both, the sequence index and some parameter that may enter the coefficients, go to infinity. A simple application is made to orthogonal matrix polynomials in the Nevai class.

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 ?f,g1,??f,g2,??f,g3, and ?f,g4 are defined and it is proved that if ??f,g1(x,y,z,w)? (resp., ??f,g3(x,y,z,w,?,?)?) is dominated by ?(x,y,z,w), 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 ??f,g2(x,y,z,w)? (resp., ??f,g4(x,y,z,w,?,?)?) is dominated by ?(x,y,z,w), then f is a generalized (resp., linear) module-𝒜 derivation and g is a (resp., linear) module-X derivation.

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.

Hlíf Árnadóttir; Thórhallur Eythórsson; Einar Freyr Sigurðsson

Stochastic evolution equations in Banachspaces with unbounded nonlinear drift and diffusion operators are considered. Under some regularity condition assumed for the solution, the rate of convergence of various numerical approximations are estimated under strong monotonicity and Lipschitz conditions. The abstract setting involves general consistency conditions and is then applied to a class of quasilinear stochastic PDEs of parabolic type.

Stochastic evolution equations in Banachspaces with unbounded nonlinear drift and diffusion operators driven by a finite dimensional Brownian motion are considered. Under some regularity condition assumed for the solution, the rate of convergence of various numerical approximations are estimated un...

Reflex latency variability was established for single motor neuron discharges in the bulbocavernosus reflex, as elicited by electrical stimuli to the dorsal penile nerve and recorded by a single fibre EMG electrode in the bulbocavernosus muscle. Whereas many reflex responses had a rather large latency variability of above 1000 microseconds (expressed as SD of mean latency) there was a group of motor neurons with a variability of around 500 microseconds. Single motor neuron reflex responses with shorter latencies tended to show less variability. No habituation of single motor neuron reflex discharges was observed on prolonged regular repetitive stimulation. Both absence of habituation and the relatively low latency variability of bulbocavernosus reflex responses for single motor neurons suggest similarities between this reflex and the first component of the blink reflex; we postulate that the shortest bulbocavernosus reflex pathway is oligosynaptic.

[en] The indefinite set-valued integral K(t) and the corresponding set of continuous functions CF are defined. Various convergence theorems have been proved for those two sets using the Hansdorff metric and the Kuratowski-Mosco convergence of sets. The density theorem of CF, the corresponding convexity theorem for F (.) and the differentiability properties of K (.) have also been studied and could be helpful in the solution of differential equations with multivalued right hand side (differential inclusions)

The paper emphasizes asymptotic behaviors, as stability, instability, dichotomy and trichotomy for skew-evolution semiflows, defined by means of evolution semiflows and evolution cocycles and which can be considered generalizations for evolution operators and skew-product semiflows. The definition a...

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 ?–growth and ?–decay, H–stability and H–instability, as well as the classic concept of exponential dichotomy.

Full Text Available In this paper we investigate some dichotomy concepts for skew-evolution semiflows in Banachspaces.Our main objective is to estab-lish relations between these concepts.We motivate our approach byillustrative examples.

A class of extended Ishikowa Iterative processes is proposed and studied, which involves many kinds of Mann and Ishikawa iterative processes. The main conclusion of the present work extends and generalizes some recent results of this research line.

Full Text Available We establish the existence and uniqueness of almost periodic solutions of a class of semilinear equations having analytic semigroups. Our basic tool in this paper is the use of fractional powers of operators.

In this note we prove that if a differentiable function oscillates between y« and « on the boundary of the unit ball then there exists a point in the interior of the ball in which the differential of the function has norm equal or less than« . This kind of approximate Rolle’s theorem is interesting ...

Azagra Rueda, Daniel; Gómez Gíl, Javier; Jaramillo Aguado, Jesus Angel

Full Text Available Abstract in spanish Estudiamos la existencia de soluciones débiles de la inclusión integral no lineal con retardos temporales múltiples. El resultado principal del artículo se basa en el Teorema de Punto Fijo de tipo Mönch y la técnica de medida de la no-compacidad débil. Abstract in english We study the existence of weak solutions for nonlinear integral inclusion with multiple time delay. The main result of the paper is based on the fixed point theorem of Mönch type and the technique of measure of weak noncompactness.

(2) is bounded for any bounded sequence $\\{ \\alpha_i \\}$. The conditions are determined ensuring (a) the solution of the corresponding homogeneous equation has an exponential estimate; (b) each solution of (1),(2) is bounded on the half-line for any bounded $f$ and bounded sequence $\\{ \\alpha_i \\}$ ; (c) $\\lim_{t \\rightarrow \\infty}x(t)=0$ for any $f, \\alpha_i$ tending to zero; (d) exponential estimate of $f$ implies a similar estimate for $x$.

Full Text Available We consider the problem of determining the unknown term in the right-hand side of a second-order differential equation with unbounded operator generating a cosine operator function from the overspecified boundary data. We obtain necessary and sufficient conditions of the unique solvability of this problem in terms of location of the spectrum of the unbounded operator and properties of its resolvent.

This ambitious and substantial monograph, written by prominent experts in the field, presents the state of the art of convexity, with an emphasis on the interplay between convex analysis and potential theory; more particularly, between Choquet theory and the Dirichlet problem. The book is unique and self-contained, and it covers a wide range of applications which will appeal to many readers.