The Experts below are selected from a list of 315 Experts worldwide ranked by ideXlab platform
Valentin Ferenczi - One of the best experts on this subject based on the ideXlab platform.
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Local Banach-Space dichotomies and ergodic Spaces
arXiv: Functional Analysis, 2020Co-Authors: W. Cuellar Carrera, N. De Rancourt, Valentin FerencziAbstract:We prove a local version of Gowers' Ramsey-type theorem [21], as well as local versions both of the Banach Space first dichotomy (the "unconditional/HI" dichotomy) of Gowers [21] and of the third dichotomy (the "minimal/tight" dichotomy) due to Ferenczi-Rosendal [18]. This means that we obtain versions of these dichotomies restricted to certain families of subSpaces called $D$-families, of which several concrete examples are given. As a main example, non-Hilbertian Spaces form $D$-families; therefore versions of the above properties for non-Hilbertian Spaces appear in new Banach Space dichotomies. As a consequence we obtain new information on the number of subSpaces of non-Hilbertian Banach Spaces, making some progress towards the "ergodic" conjecture of Ferenczi-Rosendal and towards a question of Johnson.
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Minimality, homogeneity and topological 0-1 laws for subSpaces of a Banach Space
arXiv: Functional Analysis, 2005Co-Authors: Valentin FerencziAbstract:If a Banach Space is saturated with basic sequences whose linear span embeds into the linear span of any subsequence, then it contains a minimal subSpace. It follows that any Banach Space is either ergodic or contains a minimal subSpace. For a Banach Space $X$ with an (unconditional) basis, topological 0-1 law type dichotomies are stated for block-subSpaces of $X$ as well as for subSpaces of $X$ with a successive FDD on its basis. A uniformity principle for properties of block-sequences, results about block-homogeneity, and a possible method to construct a Banach Space with an unconditional basis, which has a complemented subSpace without an unconditional basis, are deduced.
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On the number of non isomorphic subSpaces of a Banach Space
Studia Mathematica, 2005Co-Authors: Valentin Ferenczi, Christian RosendalAbstract:If a Banach Space has an unconditional basis it either contains a continuum of non isomorphic subSpaces or is isomorphic to its square and hyperplanes and satisfies other regularity properties. An HI Banach Space contains a continuum of non isomorphic subSpaces.
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a uniformly convex hereditarily indecomposable Banach Space
Israel Journal of Mathematics, 1997Co-Authors: Valentin FerencziAbstract:We construct a uniformly convex hereditarily indecomposable Banach Space, using a method similar to the one of Gowers and Maurey in [GM], and the theory of complex interpolation for a family of Banach Spaces of Coifman, Cwikel, Rochberg, Sagher, and Weiss ([CCRSW1]).
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a uniformly convex hereditarily indecomposable Banach Space
arXiv: Functional Analysis, 1995Co-Authors: Valentin FerencziAbstract:A {\em hereditarily indecomposable (or H.I.)} Banach Space is an infinite dimensional Banach Space such that no subSpace can be written as the topological sum of two infinite dimensional subSpaces. As an easy consequence, no such Space can contain an unconditional basic sequence. This notion was first introduced in 1993 by T.Gowers and B.Maurey, who constructed the first known example of a hereditarily indecomposable Space. Gowers-Maurey Space is reflexive, however it is not uniformly convex. In this article, we provide an example of a uniformly convex hereditarily indecomposable Space, using similar methods as Gowers and Maurey, and using the theory of complex interpolation for a family of Banach Spaces of Coifman, Cwikel, Rochberg, Sagher and Weiss.
Wataru Takahashi - One of the best experts on this subject based on the ideXlab platform.
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a strong convergence theorem for relatively nonexpansive mappings in a Banach Space
Journal of Approximation Theory, 2005Co-Authors: Shinya Matsushita, Wataru TakahashiAbstract:In this paper, we prove a strong convergence theorem for relatively nonexpansive mappings in a Banach Space by using the hybrid method in mathematical programming. Using this result, we also discuss the problem of strong convergence concerning nonexpansive mappings in a Hilbert Space and maximal monotone operators in a Banach Space.
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strong convergence of an iterative sequence for maximal monotone operators in a Banach Space
Abstract and Applied Analysis, 2004Co-Authors: Fumiaki Kohsaka, Wataru TakahashiAbstract:We first introduce a modified proximal point algorithm for maximal monotone operators in a Banach Space. Next, we obtain a strong convergence theorem for resolvents of maximal monotone operators in a Banach Space which generalizes the previous result by Kamimura and Takahashi in a Hilbert Space. Using this result, we deal with the convex minimization problem and the variational inequality problem in a Banach Space.
Badri Mamporia - One of the best experts on this subject based on the ideXlab platform.
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On functionals of the Wiener process in a Banach Space
Transactions of A. Razmadze Mathematical Institute, 2018Co-Authors: Badri Mamporia, Omar PurtukhiaAbstract:Abstract In development of stochastic analysis in a Banach Space one of the main problem is to establish the existence of the stochastic integral from predictable Banach Space valued (operator valued) random process. In the problem of representation of the Wiener functional as a stochastic integral we are faced with an inverse problem: we have the stochastic integral as a Banach Space valued random element and we are looking for a suitable predictable integrand process. There are positive results only for a narrow class of Banach Spaces with special geometry (UMD Banach Spaces). We consider this problem in a general Banach Space for a Gaussian functional.
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Stochastic differential equations in a Banach Space driven by the cylindrical Wiener process
Elsevier, 2017Co-Authors: Badri MamporiaAbstract:Generalized stochastic integral from predictable operator-valued random process with respect to a cylindrical Wiener process in an arbitrary Banach Space is defined. The question of existence of the stochastic integral in a Banach Space is reduced to the problem of decomposability of the generalized random element. The sufficient condition of existence of the stochastic integral in terms of p-absolutely summing operators is given. The stochastic differential equation for generalized random processes is considered and existence and uniqueness of the solution is developed. As a consequence, the corresponding results of the stochastic differential equations in an arbitrary Banach Space are given. Keywords: Ito stochastic integrals and stochastic differential equations, Wiener processes, Covariance operators in Banach Space
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Stochastic differential equations in a Banach Space driven by the cylindrical Wiener process
Transactions of A. Razmadze Mathematical Institute, 2017Co-Authors: Badri MamporiaAbstract:Abstract Generalized stochastic integral from predictable operator-valued random process with respect to a cylindrical Wiener process in an arbitrary Banach Space is defined. The question of existence of the stochastic integral in a Banach Space is reduced to the problem of decomposability of the generalized random element. The sufficient condition of existence of the stochastic integral in terms of p -absolutely summing operators is given. The stochastic differential equation for generalized random processes is considered and existence and uniqueness of the solution is developed. As a consequence, the corresponding results of the stochastic differential equations in an arbitrary Banach Space are given.
Fumiaki Kohsaka - One of the best experts on this subject based on the ideXlab platform.
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strong convergence of an iterative sequence for maximal monotone operators in a Banach Space
Abstract and Applied Analysis, 2004Co-Authors: Fumiaki Kohsaka, Wataru TakahashiAbstract:We first introduce a modified proximal point algorithm for maximal monotone operators in a Banach Space. Next, we obtain a strong convergence theorem for resolvents of maximal monotone operators in a Banach Space which generalizes the previous result by Kamimura and Takahashi in a Hilbert Space. Using this result, we deal with the convex minimization problem and the variational inequality problem in a Banach Space.
Jacek Tabor - One of the best experts on this subject based on the ideXlab platform.
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An embedding theorem for unbounded convex sets in a Banach Space
Demonstratio Mathematica, 2009Co-Authors: Jakub Bielawski, Jacek TaborAbstract:In this paper we embed the Space of nonempty closed convex subsets of a Banach Space into a Banach Space. Namely, we prove the following result: Theorem. Let X be a Banach Space, V a closed convex cone in X, dH a Hausdor distance. Let CV =fA X : A nonempty closed and convex, dH(A;V )
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an embedding theorem for unbounded convex sets in a Banach Space
Demonstratio Mathematica, 2009Co-Authors: Jakub Bielawski, Jacek TaborAbstract:In this paper we embed the Space of nonempty closed convex subsets of a Banach Space into a Banach Space. Namely, we prove the following result: Theorem. Let X be a Banach Space, V a closed convex cone in X, dH a Hausdor distance. Let CV =fA X : A nonempty closed and convex, dH(A;V ) <1g: Then CV is a commutative semigroup with cancellation law and Hausdor metric dH is positively homogeneous and invariant under translation. Consequently CV can be embedded isometrically and isomorphically as a convex cone into a Banach Space.
