Banach

banach@mathdept.okstate.edu

2549 discussions

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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Abstract of a paper by Sonia Berrios and Geraldo Botelho
by alspach＠fourier.math.okstate.edu 30 Sep '10

30 Sep '10

This is an announcement for the paper "Approximation properties determined by operator ideals" by Sonia Berrios and Geraldo Botelho. Abstract: Given an operator ideal I, a Banach space E has the I-approximation property if operators on E can be uniformly approximated on compact subsets of E by operators belonging to I. In this paper the I- approximation property is studied in projective tensor products, spaces of linear functionals, spaces of homogeneous polynomials (in particular, spaces of linear operators), spaces of holomorphic functions and their preduals. Archive classification: math.FA Remarks: 24 pages Submitted from: botelho(a)ufu.br The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1009.2977 or http://arXiv.org/abs/1009.2977

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Abstract of a paper by Niels Jakob Laustsen, Edward Odell, Thomas Schlumprecht, and Andras Zsak
by alspach＠fourier.math.okstate.edu 30 Sep '10

30 Sep '10

This is an announcement for the paper "Dichotomy theorems for random matrices and closed ideals of operators on $\big(\bigoplus _{n=1}^\infty\ell_1^n \big)_{\mathrm{c}_0}$" by Niels Jakob Laustsen, Edward Odell, Thomas Schlumprecht, and Andras Zsak. Abstract: We prove two dichotomy theorems about sequences of operators into $L_1$ given by random matrices. In the second theorem we assume that the entries of each random matrix form a sequence of independent, symmetric random variables. Then the corresponding sequence of operators either uniformly factor the identity operators on $\ell_1^k$ $(k\in\mathbb N$) or uniformly approximately factor through $\mathrm{c}_0$. The first theorem has a slightly weaker conclusion still related to factorization properties but makes no assumption on the random matrices. Indeed, it applies to operators defined on an arbitrary sequence of Banach spaces. These results provide information on the closed ideal structure of the Banach algebra of all operators on the space $\big(\bigoplus_{n=1}^\infty\ell_1^n \big)_{\mathrm{c}_0}$. Archive classification: math.FA Mathematics Subject Classification: 47L10 (primary), 46B09, 46B42, 47L20, 46B45 (secondary) Remarks: 22 pages Submitted from: andras.zsak(a)maths.nottingham.ac.uk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1009.2923 or http://arXiv.org/abs/1009.2923

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Abstract of a paper by Daniel Pellegrino
by alspach＠fourier.math.okstate.edu 30 Sep '10

30 Sep '10

This is an announcement for the paper "A note on the best constants for the Bohnenblust-Hille inequality" by Daniel Pellegrino. Abstract: In this note we show that a recent new proof of Bohnenblust-Hille inequality, due to Defant et al, combined with the better known constant for Littlewood 4/3 theorem and the optimal constants of Khinchin inequality, due to Haagerup, provide quite better estimates for the constants involved in the Bohnenblust-Hille inequality. For example, if $2\leq m\leq13,$ we show that the constants $C_{m}=2^{(m-1)/2}$ can be replaced by $2^{\frac{m^{2}+m-6}{4m}% }K_{G}^{2/m}$, which are substantially better than $C_{m}$ (here $K_{G}$ denotes the complex Grothendieck Archive classification: math.FA Remarks: 7 pages Submitted from: dmpellegrino(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1009.2717 or http://arXiv.org/abs/1009.2717

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