Banach October 2010

banach@mathdept.okstate.edu

4 participants
18 discussions

Abstract of a paper by Andrea Marchese and Clemente Zanco
by alspach＠fourier.math.okstate.edu 18 Oct '10

18 Oct '10

This is an announcement for the paper "On a question by Corson about point-finite coverings" by Andrea Marchese and Clemente Zanco. Abstract: We answer in the affirmative the following question raised by H. H. Corson in 1961: "Is it possible to cover every Banach space X by bounded convex sets with nonempty interior in such a way that no point of X belongs to infinitely many of them?" Actually we show the way to produce in every Banach space X a bounded convex tiling of order 2, i.e. a covering of X by bounded convex closed sets with nonempty interior (tiles) such that the interiors are pairwise disjoint and no point of X belongs to more than two tiles. Archive classification: math.FA Remarks: to appear on Israel J. Math Submitted from: marchese(a)mail.dm.unipi.it The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1009.4681 or http://arXiv.org/abs/1009.4681

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Abstract of a paper by Ramon van Handel
by alspach＠fourier.math.okstate.edu 18 Oct '10

18 Oct '10

This is an announcement for the paper "The universal Glivenko-Cantelli property" by Ramon van Handel. Abstract: Let F be a separable uniformly bounded family of measurable functions on a standard measurable space, and let N_{[]}(F,\epsilon,\mu) be the smallest number of \epsilon-brackets in L^1(\mu) needed to cover F. The following are equivalent: 1. F is a universal Glivenko-Cantelli class. 2. N_{[]}(F,\epsilon,\mu)<\infty for every \epsilon>0 and every probability measure \mu. 3. F is totally bounded in L^1(\mu) for every probability measure \mu. 4. F does not contain a Boolean \sigma-independent sequence. In particular, universal Glivenko-Cantelli classes are uniformity classes for general sequences of almost surely convergent random measures. Archive classification: math.PR math.FA math.MG math.ST stat.TH Mathematics Subject Classification: 60F15, 60B10, 41A46 Remarks: 15 pages Submitted from: rvan(a)princeton.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1009.4434 or http://arXiv.org/abs/1009.4434

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Abstract of a paper by Timur Oikhberg
by alspach＠fourier.math.okstate.edu 18 Oct '10

18 Oct '10

This is an announcement for the paper "Rate of decay of s-numbers" by Timur Oikhberg. Abstract: For an operator $T \in B(X,Y)$, we denote by $a_m(T)$, $c_m(T)$, $d_m(T)$, and $t_m(T)$ its approximation, Gelfand, Kolmogorov, and absolute numbers. We show that, for any infinite dimensional Banach spaces $X$ and $Y$, and any sequence $\alpha_m \searrow 0$, there exists $T \in B(X,Y)$ for which the inequality $$ 3 \alpha_{\lceil m/6 \rceil} \geq a_m(T) \geq \max\{c_m(t), d_m(T)\} \geq \min\{c_m(t), d_m(T)\} \geq t_m(T) \geq \alpha_m/9 $$ holds for every $m \in \N$. Similar results are obtained for other $s$-scales. Archive classification: math.FA math.NA Mathematics Subject Classification: 46A3, 46B28, 47B10 Submitted from: toikhber(a)math.uci.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1009.4278 or http://arXiv.org/abs/1009.4278

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Abstract of a paper by Paul F. X. Mueller
by alspach＠fourier.math.okstate.edu 18 Oct '10

18 Oct '10

This is an announcement for the paper "A thin-thick decomposition for Hardy martingales" by Paul F. X. Mueller. Abstract: We prove thin-thick decompositions, for the class of Hardy martingales and thereby strengthen its square function characterization. We apply the underlying method to several classical martingale inequalities, for which we give new proofs . Archive classification: math.FA Submitted from: pfxm(a)bayou.uni-linz.ac.at The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1009.3629 or http://arXiv.org/abs/1009.3629

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Abstract of a paper by Timur Oikhberg and Christian Rosendal
by alspach＠fourier.math.okstate.edu 18 Oct '10

18 Oct '10

This is an announcement for the paper "Subspace structure of some operator and Banach spaces" by Timur Oikhberg and Christian Rosendal. Abstract: We construct a family of separable Hilbertian operator spaces, such that the relation of complete isomorphism between the subspaces of each member of this family is complete $\ks$. We also investigate some interesting properties of completely unconditional bases of the spaces from this family. In the Banach space setting, we construct a space for which the relation of isometry of subspaces is equivalent to equality of real numbers. Archive classification: math.FA math.LO Remarks: 30 pages Submitted from: toikhber(a)math.uci.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1009.3591 or http://arXiv.org/abs/1009.3591

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Abstract of a paper by Shlomo Reisner, Carsten Schutt and Elisabeth M. Werner
by alspach＠fourier.math.okstate.edu 18 Oct '10

18 Oct '10

This is an announcement for the paper "A note on Mahler's conjecture" by Shlomo Reisner, Carsten Schutt and Elisabeth M. Werner. Abstract: Let $K$ be a convex body in $\mathbb{R}^n$ with Santal\'o point at $0$. We show that if $K$ has a point on the boundary with positive generalized Gau{\ss} curvature, then the volume product $|K| |K^\circ|$ is not minimal. This means that a body with minimal volume product has Gau{\ss} curvature equal to $0$ almost everywhere and thus suggests strongly that a minimal body is a polytope. Archive classification: math.FA Mathematics Subject Classification: 52A20 Submitted from: elisabeth.werner(a)case.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1009.3583 or http://arXiv.org/abs/1009.3583

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Abstract of a paper by Amir Nasseri
by alspach＠fourier.math.okstate.edu 18 Oct '10

18 Oct '10

This is an announcement for the paper "On the existence of J-class operators" by Amir Nasseri. Abstract: In this note we answer in the negative the question raised by G.Costakis and A.Manoussos, whether there exists a J-class operator on every non-separable Banach space. In par- ticular we show that there exists a non-separable Banach space constructed by A.Arvanitakis, S.Argyros and A.Tolias such that the J-set of every operator on this space has empty interior for each non-zero vector. On the other hand, on non-separable spaces which are reflexive there always exist a J-class operator. Archive classification: math.FA Remarks: 8 pages, hypercyclicity, J-class operators Submitted from: amir.nasseri(a)uni-dortmund.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1009.3461 or http://arXiv.org/abs/1009.3461

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N. Kalton
by Fritz Gesztesy 17 Oct '10

17 Oct '10

Dear Colleagues, The Department of Mathematics of the University of Missouri, Columbia, MO, is in the process of establishing a website in honor of Nigel Kalton, who passed away recently. The website will consist of several parts. We hope to be able to post downloadable pdf files of his works, supply a list of his students and co-authors, indicate his editorial activity, establish a photo gallery, and comment on some of his other significant activities, such as playing chess. We also plan to have a section in which students, collaborators, and friends will be able to recall fond reminiscences and express their appreciation of Nigel. Apart from alerting you to this activity, the purpose of this message is to solicit contributions you may be able to make to this Kalton Memorial Website, such as, photos, stories, reminiscences, etc. Please send all material to Fritz Gesztesy Department of Mathematics University of Missouri Columbia, MO 65211 USA E-mail: gesztesyf(a)missouri.edu Thanks, and best regards, Fritz Gesztesy PLEASE NOTE THE CHANGE OF E-MAIL ADDRESS: gesztesyf(a)missouri.edu Department of Mathematics, University of Missouri, Columbia, MO 65211, USA Office: (573) 882 4386 FAX: (573) 882 1869 Department: (573) 882 6221 Home: (573) 443 8913 E-mail: gesztesyf(a)missouri.edu http://www.math.missouri.edu/personnel/faculty/gesztesyf.html

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Banach October 2010