July 2010 - Banach - mathdept.okstate.edu

Abstract of a paper by Iryna Banakh and Taras Banakh
by alspach＠fourier.math.okstate.edu 14 Jul '10

14 Jul '10

This is an announcement for the paper "Constructing non-compact operators into $c_0$" by Iryna Banakh and Taras Banakh. Abstract: We prove that for each dense non-compact linear operator $S:X\to Y$ between Banach spaces there is a linear operator $T:Y\to c_0$ such that the operator $TS:X\to c_0$ is not compact. This generalizes the Josefson-Nissenzweig Theorem. Archive classification: math.FA Mathematics Subject Classification: 47B07, 46B15 Remarks: 2 pages Submitted from: tbanakh(a)yahoo.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1006.3089 or http://arXiv.org/abs/1006.3089

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Abstract of a paper by Jesus Araujo and Luis Dubarbie
by alspach＠fourier.math.okstate.edu 14 Jul '10

14 Jul '10

This is an announcement for the paper "Noncompactness and noncompleteness in isometries of Lipschitz spaces" by Jesus Araujo and Luis Dubarbie. Abstract: We solve the following two questions concerning surjective linear isometries between spaces of Lipschitz functions $\mathrm{Lip}(X,E)$ and $\mathrm{Lip}(Y,F)$, for strictly convex normed spaces $E$ and $F$ and metric spaces $X$ and $Y$: \begin{enumerate} \item Characterize those base spaces $X$ and $Y$ for which all isometries are weighted composition maps. \item Give a condition independent of base spaces under which all isometries are weighted composition maps. \end{enumerate} In particular, we prove that requirements of completeness on $X$ and $Y$ are not necessary when $E$ and $F$ are not complete, which is in sharp contrast with results known in the scalar context. We also give the special form of this kind of isometries. Archive classification: math.FA Mathematics Subject Classification: 2010: 47B33 (Primary), 46B04, 46E15, 46E40, 47B38 (Secondary) Remarks: 14 pages, no figures, \documentclass[12pt]{amsart} Submitted from: araujoj(a)unican.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1006.2995 or http://arXiv.org/abs/1006.2995

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Abstract of a paper by Sergey Bobkov, Mokshay Madiman, and Liyao Wang
by alspach＠fourier.math.okstate.edu 14 Jul '10

14 Jul '10

This is an announcement for the paper "Fractional generalizations of Young and Brunn-Minkowski inequalities" by Sergey Bobkov, Mokshay Madiman, and Liyao Wang. Abstract: A generalization of Young's inequality for convolution with sharp constant is conjectured for scenarios where more than two functions are being convolved, and it is proven for certain parameter ranges. The conjecture would provide a unified proof of recent entropy power inequalities of Barron and Madiman, as well as of a (conjectured) generalization of the Brunn-Minkowski inequality. It is shown that the generalized Brunn-Minkowski conjecture is true for convex sets; an application of this to the law of large numbers for random sets is described. Archive classification: math.FA cs.IT math.IT math.PR Remarks: 17 pages Submitted from: mokshay.madiman(a)yale.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1006.2884 or http://arXiv.org/abs/1006.2884

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Abstract of a paper by Pandelis Dodos, Jordi Lopez-Abad and Stevo Todorcevic
by alspach＠fourier.math.okstate.edu 06 Jul '10

06 Jul '10

This is an announcement for the paper "Banach spaces and Ramsey theory: some open problems" by Pandelis Dodos, Jordi Lopez-Abad and Stevo Todorcevic. Abstract: We discuss some open problems in the Geometry of Banach spaces having Ramsey-theoretic flavor. The problems are exposed together with well known results related to them. Archive classification: math.FA math.CO Remarks: 17 pages, no figures; RACSAM, to appear Submitted from: pdodos(a)math.uoa.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1006.2668 or http://arXiv.org/abs/1006.2668

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Abstract of a paper by Pandelis Dodos
by alspach＠fourier.math.okstate.edu 06 Jul '10

06 Jul '10

This is an announcement for the paper "Operators whose dual has non-separable range" by Pandelis Dodos. Abstract: Let $X$ and $Y$ be separable Banach spaces and $T:X\to Y$ be a bounded linear operator. We characterize the non-separability of $T^*(Y^*)$ by means of fixing properties of the operator $T$. Archive classification: math.FA Remarks: 20 pages, no figures Submitted from: pdodos(a)math.uoa.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1006.2666 or http://arXiv.org/abs/1006.2666

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Abstract of a paper by Kevin Benaland and Pandelis Dodos
by alspach＠fourier.math.okstate.edu 06 Jul '10

06 Jul '10

This is an announcement for the paper "On strictly singular operators between separable Banach spaces" by Kevin Beanland and Pandelis Dodos. Abstract: Let $X$ and $Y$ be separable Banach spaces 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 Banach space $Y_p$ 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. Archive classification: math.FA Remarks: 20 pages, no figures; Mathematika, to appear Submitted from: pdodos(a)math.uoa.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1006.2672 or http://arXiv.org/abs/1006.2672

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Abstract of a paper by Pandelis Dodos
by alspach＠fourier.math.okstate.edu 06 Jul '10

06 Jul '10

This is an announcement for the paper "Quotients of Banach spaces and surjectively universal spaces" by Pandelis Dodos. Abstract: We characterize those classes $\mathcal{C}$ of separable Banach spaces for which there exists a separable Banach space $Y$ not containing $\ell_1$ and such that every space in the class $\mathcal{C}$ is a quotient of $Y$. Archive classification: math.FA Citation: Studia Mathematica 197 (2010), 171-194 Remarks: 23 pages, no figures Submitted from: pdodos(a)math.uoa.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1006.2665 or http://arXiv.org/abs/1006.2665

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New Journal - Annals of Functional Analysis
by Dale Alspach 06 Jul '10

06 Jul '10

Dear colleague, It is my pleasure to invite you to submit a research paper of high standard or critical survey paper for possible publication in the electronic journal. "Annals of Functional Analysis (AFA)" http://www.emis.de/journals/AFA/ It would be appreciated if you promote the journal among your fellow-workers and colleagues. Best wishes M. S. Moslehian Editor-in-chief of AFA ********************************************** Mohammad Sal Moslehian Ph.D., Professor of Mathematics Address: Dept. of Pure Math., P.O. Box 1159 Ferdowsi University of Mashhad Mashhad 91775, Iran Mobile: (+98)(9151140894) Tel-Fax: (+98)(511)(8828606) E-mails: moslehian(a)ams.org moslehian(a)um.ac.ir Home: http://www.um.ac.ir/~moslehian/ **********************************************

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Abstract of a paper by Catalin Badea, Sophie Grivaux and Vladimir Muller
by alspach＠fourier.math.okstate.edu 04 Jul '10

04 Jul '10

This is an announcement for the paper "The rate of convergence in the method of alternating projections" by Catalin Badea, Sophie Grivaux and Vladimir Muller. Abstract: A generalization of the cosine of the Friedrichs angle between two subspaces to a parameter associated to several closed subspaces of a Hilbert space is given. This parameter is used to analyze the rate of convergence in the von Neumann-Halperin method of cyclic alternating projections. General dichotomy theorems are proved, in the Hilbert or Banach space situation, providing conditions under which the alternative QUC/ASC (quick uniform convergence versus arbitrarily slow convergence) holds. Several meanings for ASC are proposed. Archive classification: math.FA math.NA Remarks: 23 pages, to appear in St. Petersburg Math J. (2010) Submitted from: catalin.badea(a)math.univ-lille1.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1006.2047 or http://arXiv.org/abs/1006.2047

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Abstract of a paper by Catalin Badea and Yuri I. Lyubich
by alspach＠fourier.math.okstate.edu 04 Jul '10

04 Jul '10

This is an announcement for the paper "Geometric, spectral and asymptotic properties of averaged products of projections in Banach spaces" by Catalin Badea and Yuri I. Lyubich. Abstract: According to the von Neumann-Halperin and Lapidus theorems, in a Hilbert space the iterates of products or, respectively, of convex combinations of orthoprojections are strongly convergent. We extend these results to the iterates of convex combinations of products of some projections in a complex Banach space. The latter is assumed uniformly convex or uniformly smooth for the orthoprojections, or reflexive for more special projections, in particular, for the hermitian ones. In all cases the proof of convergence is based on a known criterion in terms of the boundary spectrum. Archive classification: math.FA Remarks: 22 pages Submitted from: catalin.badea(a)math.univ-lille1.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1006.2052 or http://arXiv.org/abs/1006.2052

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