Banach

banach@mathdept.okstate.edu

2549 discussions

Abstract of a paper by Benoit Kloeckner
by alspach＠math.okstate.edu 27 Feb '13

27 Feb '13

This is an announcement for the paper "Yet another short proof of Bourgain's distorsion estimate" by Benoit Kloeckner. Abstract: We use a self-improvement argument to give a very short and elementary proof of the result of Bourgain saying that regular trees do not admit bi-Lipschitz embeddings into uniformly convex Banach spaces. Archive classification: math.FA math.MG Report Number: IFPREPUB Remarks: 2 pages. Submitted from: benoit.kloeckner(a)ens-lyon.org The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1302.1738 or http://arXiv.org/abs/1302.1738

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Abstract of a paper by Wieslaw Kubis, Anibal Molto, and Stanimir Troyanski
by alspach＠math.okstate.edu 27 Feb '13

27 Feb '13

This is an announcement for the paper "Topological properties of the continuous function spaces on some ordered compacta" by Wieslaw Kubis, Anibal Molto, and Stanimir Troyanski. Abstract: Some new classes of compacta $K$ are considered for which $C(K)$ endowed with the pointwise topology has a countable cover by sets of small local norm--diameter. Archive classification: math.FA math.GN Mathematics Subject Classification: 46B26, 03G10 Remarks: 11 pages Submitted from: kubis(a)math.cas.cz The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1302.0829 or http://arXiv.org/abs/1302.0829

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Abstract of a paper by Vitali Milman and Liran Rotem
by alspach＠math.okstate.edu 27 Feb '13

27 Feb '13

This is an announcement for the paper "alpha-concave functions and a functional extension of mixed volumes" by Vitali Milman and Liran Rotem. Abstract: Mixed volumes, which are the polarization of volume with respect to the Minkowski addition, are fundamental objects in convexity. In this note we announce the construction of mixed integrals, which are functional analogs of mixed volumes. We build a natural addition operation + on the class of quasi-concave functions, such that every class of \alpha-concave functions is closed under +. We then define the mixed integrals, which are the polarization of the integral with respect to +. We proceed to discuss the extension of various classic inequalities to the functional setting. For general quasi-concave functions, this is done by restating those results in the language of rearrangement inequalities. Restricting ourselves to \alpha-concave functions, we state a generalization of the Alexandrov inequalities in their more familiar form. Archive classification: math.FA math.MG Citation: Electron. Res. Announc. Math. Sci. 20 (2013), 1-11 Submitted from: liranro1(a)post.tau.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1302.0823 or http://arXiv.org/abs/1302.0823

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Abstract of a paper by Spiros A. Argyros and Pavlos Motakis
by alspach＠math.okstate.edu 27 Feb '13

27 Feb '13

This is an announcement for the paper "Non separable reflexive spaces admitting $\ell_1$ as a unique spreading model" by Spiros A. Argyros and Pavlos Motakis. Abstract: Examples of non separable reflexive Banach spaces $\mathfrak{X}_{2^{\aleph_0}}$, admitting only $\ell_1$ as a spreading model, are presented. The definition of the spaces is based on $\alpha$-large, $\alpha<\omega_1$ compact families of finite subsets of the continuum. We show the existence of such families and we study their properties. Moreover, based on those families we construct a reflexive space $\mathfrak{X}_{2^{\aleph_0}}^\alpha$, $\alpha<\omega_1$ with density the continuum, such that every bounded non norm convergent sequence $\{x_k\}_k$ has a subsequence generating $\ell_1^\alpha$ as a spreading model. Archive classification: math.FA math.CO Mathematics Subject Classification: 46B03, 46B06, 46B26, 03E05 Remarks: 23 pages, no figures Submitted from: pmotakis(a)central.ntua.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1302.0715 or http://arXiv.org/abs/1302.0715

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Abstract of a paper by V. P. Fonf, A. J. Pallares, R. J. Smith, and S. Troyanski
by alspach＠math.okstate.edu 27 Feb '13

27 Feb '13

This is an announcement for the paper "Polyhedrality in Pieces" by V. P. Fonf, A. J. Pallares, R. J. Smith, and S. Troyanski. Abstract: The aim of this paper is to present two tools, Theorems 4 and 7, that make the task of finding equivalent polyhedral norms on certain Banach spaces easier and more transparent. The hypotheses of both tools are based on countable decompositions, either of the unit sphere S_X or of certain subsets of the dual ball of a given Banach space X. The sufficient conditions of Theorem 4 are shown to be necessary in the separable case. Using Theorem 7, we can unify two known results regarding the polyhedral renorming of certain C(K) spaces, and spaces having an (uncountable) unconditional basis. New examples of spaces having equivalent polyhedral norms are given in the fi?nal section. Archive classification: math.FA Submitted from: apall(a)um.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1302.0160 or http://arXiv.org/abs/1302.0160

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Abstract of a paper by Vladimir Temlyakov
by alspach＠math.okstate.edu 27 Feb '13

27 Feb '13

This is an announcement for the paper "An inequality for the entropy numbers and its application" by Vladimir Temlyakov. Abstract: We prove an inequality for the entropy numbers in terms of nonlinear Kolmogorov's widths. This inequality is in a spirit of known inequalities of this type and it is adjusted to the form convenient in applications for $m$-term approximations with respect to a given system. Also, we obtain upper bounds for the $m$-term approximation by the Weak Relaxed Greedy Algorithm with respect to a system which is not a dictionary. Archive classification: math.MG math.FA Submitted from: n.i.pentacaput(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1301.7624 or http://arXiv.org/abs/1301.7624

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Abstract of a paper by Balint Farkas
by alspach＠math.okstate.edu 30 Jan '13

30 Jan '13

This is an announcement for the paper "A Bohl--Bohr--Kadets type theorem characterizing Banach spaces not containing $c_0$" by Balint Farkas. Abstract: We prove that a separable Banach space $E$ does not contain a copy of the space $\co$ of null-sequences if and only if for every doubly power-bounded operator $T$ on $E$ and for every vector $x\in E$ the relative compactness of the sets $\{T^{n+m}x-T^nx: n\in \NN\}$ (for some/all $m\in\NN$, $m\geq 1$) and $\{T^nx:n\in \NN\}$ are equivalent. With the help of the Jacobs--de Leeuw--Glicksberg decomposition of strongly compact semigroups the case of (not necessarily invertible) power-bounded operators is also handled. Archive classification: math.FA Mathematics Subject Classification: 47A99, 46B04, 43A60 Submitted from: farkasb(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1301.6250 or http://arXiv.org/abs/1301.6250

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Abstract of a paper by Sophie Grivaux and Maria Roginskaya
by alspach＠math.okstate.edu 30 Jan '13

30 Jan '13

This is an announcement for the paper "On Read's type operators on Hilbert spaces" by Sophie Grivaux and Maria Roginskaya. Abstract: Using Read's construction of operators without non-trivial invariant subspaces/subsets on $\ell_{1}$ or $c_{0}$, we construct examples of operators on a Hilbert space whose set of hypercyclic vectors is ``large'' in various senses. We give an example of an operator such that the closure of every orbit is a closed subspace, and then, answering a question of D. Preiss, an example of an operator such that the set of its non-hypercyclic vectors is Gauss null. This operator has the property that it is orbit-unicellular, i.e. the family of the closures of its orbits is totally ordered. We also exhibit an example of an operator on a Hilbert space which is not orbit-reflexive. Archive classification: math.FA Citation: Int. Math. Res. Not., 2008 Art. ID rnn083, 42 pp Remarks: This is a preprint version of the article "On Read's type The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1301.6226 or http://arXiv.org/abs/1301.6226

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Abstract of a paper by Sophie Grivaux and Maria Roginskaya
by alspach＠math.okstate.edu 30 Jan '13

30 Jan '13

This is an announcement for the paper "An example of a minimal action of the free semi-group $\F^{+}_{2}$ on the Hilbert space" by Sophie Grivaux and Maria Roginskaya. Abstract: The Invariant Subset Problem on the Hilbert space is to know whether there exists a bounded linear operator $T$ on a separable infinite-dimensional Hilbert space $H$ such that the orbit $\{T^{n}x;\ n\ge 0\}$ of every non-zero vector $x\in H$ under the action of $T$ is dense in $H$. We show that there exists a bounded linear operator $T$ on a complex separable infinite-dimensional Hilbert space $H$ and a unitary operator $V$ on $H$, such that the following property holds true: for every non-zero vector $x\in H$, either $x$ or $Vx$ has a dense orbit under the action of $T$. As a consequence, we obtain in particular that there exists a minimal action of the free semi-group with two generators $\F^{+}_{2}$ on a complex separable infinite-dimensional Hilbert space $H$. Archive classification: math.FA math.DS Remarks: 10 p Submitted from: grivaux(a)math.univ-lille1.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1301.6144 or http://arXiv.org/abs/1301.6144

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Abstract of a paper by Sophie Grivaux and Maria Roginskaya
by alspach＠math.okstate.edu 30 Jan '13

30 Jan '13

This is an announcement for the paper "A general approach to Read's type constructions of operators without non-trivial invariant closed subspaces" by Sophie Grivaux and Maria Roginskaya. Abstract: We present a general method for constructing operators without non-trivial invariant closed subsets on a large class of non-reflexive Banach spaces. In particular, our approach unifies and generalizes several constructions due to Read of operators without non-trivial invariant subspaces on the spaces $\ell_{1}$, $c_{0}$ or $\oplus_{\ell_{2}}J$, and without non-trivial invariant subsets on $\ell_{1}$. We also investigate how far our methods can be extended to the Hilbertian setting, and construct an operator on a quasireflexive dual Banach space which has no non-trivial $w^{*}$-closed invariant subspace. Archive classification: math.FA Remarks: 62 p Submitted from: grivaux(a)math.univ-lille1.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1301.6143 or http://arXiv.org/abs/1301.6143

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