Banach

banach@mathdept.okstate.edu

2549 discussions

SUMIRFAS-2nd announcement
by Bill Johnson 25 Jul '12

25 Jul '12

2nd ANNOUNCEMENT OF SUMIRFAS 2012 The Informal Regional Functional Analysis Seminar August 3-5 Texas A&M University, College Station Schedule: Talks for SUMIRFAS will be posted on the Workshop in Analysis and Probability page, whose NEW URL is http://www.math.tamu.edu/~kerr/workshop/ The first talk will be in the early afternoon on Friday and the Seminar concludes by lunch time on Sunday. All talks will be in Blocker 169. The Blocker Building is on Ireland St. just south of University Dr. on the Texas A&M campus: http://www.math.tamu.edu/contact/blocker.html. Coffee and refreshments will be available in Blocker 148. Speakers at SUMIRFAS 2012 include Pete Casazza The Kadison-Singer Problem in Mathematics and Engineering Ed Effros Grothendieck and Quantized Functional Analysis Su Gao Universal equivalence relations from actions of the unitary group Ali Kavruk Relative Riesz Interpolations in C*-algebra Theory Masoud Khalkhali Spectral Zeta Functions and Scalar Curvature for Noncommutative Tori Izabella Laba Buffon's needle estimates for rational product Cantor sets Michael Lacey On the two weight inequality for the Hilbert transform Paul Mueller A Davis Decomposition for Hardy Martingales Darrin Speegle The HRT conjecture for functions with sufficiently fast decay Russ Thompson An introduction to the rate of escape of random walks on groups August 6-10 there will be a Concentration Week on "Recent advances in Harmonic Analysis and Spectral Theory", organized by Andrew Comech, David Damanik, Constanze Liaw (chair), and Alexei Poltoratski. This CW is designed to bring together two groups of experts: those specializing in complex and harmonic analysis and those working in spectral theory of differential operators and mathematical physics. The main goals of the CW are to study new relationships and to widen further participation in this area in the United States. Introductory series of lectures by Stephen Gustafson, Svetlana Jitomirskaya, Helge Krueger, and Brett Wick are planned to acquaint non-experts with these topics with the reasonable expectation that some the participants in the larger Workshop will will be attracted to this program and inject new ideas into the area. The home page for this Workshop is at http://www.math.tamu.edu/~comech/events/hast-2012/ The Workshop is supported in part by grants from the National Science Foundation (NSF). Minorities, women, graduate students, and young researchers are especially encouraged to attend. For logistical support, including requests for support, please contact Cara Barton <cara(a)math.tamu.edu>. For more information on the Workshop itself, please contact William Johnson <johnson(a)math.tamu.edu>, David Kerr <kerr(a)math.tamu.edu>, or Gilles Pisier <pisier(a)math.tamu.edu>. For information about the Concentration Week on "Recent advances in Harmonic Analysis and Spectral Theory" contact Constanze Liaw <conni(a)math.tamu.edu>

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Conference honoring Prof. I Namioka
by zpiotr＠as.ysu.edu 17 Jul '12

17 Jul '12

Dear Colleagues, As you might have read in the recent notices of the AMS, we are organizing a Special Session "Separate versus Joint Continuity - a tribute to Prof. I. Namioka" during the AMS Central Fall Sectional Meeting at the University of Akron, OH, October 20-21, 2012. In celebration of the coming 50th anniversary of the appearance of his monumental "Linear topological spaces", on Friday afternoon, October 19 (a day before the Akron Meeting) we want to honor Prof. Namioka by slating a mathematical gathering at Kent State University (a different location!) and we hope you can make it. We have contacted Prof. I. Namioka and he has kindly agreed to give a talk at Friday's meeting. We warmly invite you to attend these special events, both at KSU and Akron. We have a very limited number of slots available for a 20 minute presentation, so if you are interested in giving a talk/announcment please contact us ASAP. Regardless, whether you give a talk or not, we hope you can attend. On behalf of the Special Session Organizing Committee Dr. Zbigniew Piotrowski

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Abstract of a paper by Gilles Godefroy, Gilles Lancien and Vaclav Zizler
by alspach＠math.okstate.edu 13 Jul '12

13 Jul '12

This is an announcement for the paper "The non-linear geometry of Banach spaces after Nigel Kalton" by Gilles Godefroy, Gilles Lancien and Vaclav Zizler. Abstract: This is a survey of some of the results which were obtained in the last twelve years on the non-linear geometry of Banach spaces. We focus on the contribution of the late Nigel Kalton. Archive classification: math.FA Submitted from: gilles.lancien(a)univ-fcomte.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1207.2958 or http://arXiv.org/abs/1207.2958

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Abstract of a paper by Jose Luis Gamez-Merino and Juan B. Seoane-Sepulveda
by alspach＠math.okstate.edu 13 Jul '12

13 Jul '12

This is an announcement for the paper "An undecidable case of lineability in R^R" by Jose Luis Gamez-Merino and Juan B. Seoane-Sepulveda. Abstract: Recently it has been proved that, assuming that there is an almost disjoint family of cardinality $2^{\mathfrak c}$ in $\mathfrak c$ (which is assured, for instance, by either Martin's Axiom, or CH, or even \mbox{$2^{<\mathfrak c}=\mathfrak c$}) one has that the set of Sierpi\'nski-Zygmund functions is $2^{\mathfrak{c}}$-strongly algebrable (and, thus, $2^{\mathfrak{c}}$-lineable). Here we prove that these two statements are actually equivalent and, moreover, they both are undecidable. This would be the first time in which one encounters an undecidable proposition in the recently coined theory of lineability. Archive classification: math.FA math.LO Mathematics Subject Classification: 03E50, 03E75, 15A03, 26A15 Remarks: 5 pages Submitted from: jseoane(a)mat.ucm.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1207.2906 or http://arXiv.org/abs/1207.2906

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Abstract of a paper by Daniel Nunez-Alarcon and Daniel Pellegrino
by alspach＠math.okstate.edu 13 Jul '12

13 Jul '12

This is an announcement for the paper "A simple proof that the power $\frac{2m}{m+1}$ in the Bohnenblust--Hille inequalities is sharp" by Daniel Nunez-Alarcon and Daniel Pellegrino. Abstract: The power $\frac{2m}{m+1}$ in the polynomial (and multilinear) Bohnenblust--Hille inequality is optimal. This result is well-known but its proof highly nontrivial. In this note we present a quite simple proof of this fact. Archive classification: math.FA Submitted from: dmpellegrino(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1207.2662 or http://arXiv.org/abs/1207.2662

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Abstract of a paper by Richard Lechner
by alspach＠math.okstate.edu 13 Jul '12

13 Jul '12

This is an announcement for the paper "The one-third-trick and shift operators" by Richard Lechner. Abstract: In this paper we obtain a representation as martingale transform operators for the rearrangement and shift operators introduced by T. Figiel. The martingale transforms and the underlying sigma algebras are obtained explicitly by combinatorial means. The known norm estimates for those operators are a direct consequence of our representation. Archive classification: math.FA Submitted from: lechner(a)bayou.uni-linz.ac.at The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1207.2347 or http://arXiv.org/abs/1207.2347

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Abstract of a paper by Anil Kumar Karn and Deba Prasad Sinha
by alspach＠math.okstate.edu 13 Jul '12

13 Jul '12

This is an announcement for the paper "Compactness and an approximation property related to an operator ideal" by Anil Kumar Karn and Deba Prasad Sinha. Abstract: For an operator ideal $\mathcal A$, we study the composition operator ideals ${\mathcal A}\circ{\mathcal K}$, ${\mathcal K}\circ{\mathcal A}$ and ${\mathcal K}\circ{\mathcal A}\circ{\mathcal K}$, where $\mathcal K$ is the ideal of compact operators. We introduce a notion of an $\mathcal A$-approximation property on a Banach space and characterise it in terms of the density of finite rank operators in ${\mathcal A}\circ{\mathcal K}$ and ${\mathcal K}\circ{\mathcal A}$. We propose the notions of $\ell _{\infty}$-extension and $\ell_1$-lifting properties for an operator ideal $\mathcal A$ and study ${\mathcal A}\circ{\mathcal K}$, ${\mathcal }\circ{\mathcal A}$ and the $\mathcal A$-approximation property where $\mathcal A$ is injective or surjective and/or with the $\ell _{\infty}$-extension or $\ell _1$-lifting property. In particular, we show that if $\mathcal A$ is an injective operator ideal with the $\ell _\infty$-extension property, then we have: {\item{(a)} $X$ has the $\mathcal A$-approximation property if and only if $({\mathcal A}^{min})^{inj}(Y,X)={\mathcal A}^{min}(Y,X)$, for all Banach spaces $Y$. \item{(b)} The dual space $X^*$ has the $\mathcal A$-approximation property if and only if $(({\mathcal A}^{dual})^{min})^{sur}(X,Y)=({\mathcal A}^{dual})^{min}(X,Y)$, for all Banach spaces $Y$.}For an operator ideal $\mathcal A$, we study the composition operator ideals ${\mathcal A}\circ{\mathcal K}$, Archive classification: math.FA Mathematics Subject Classification: Primary 46B50, Secondary 46B20, 46B28, 47B07 Remarks: 23 pages Submitted from: anilkarn(a)niser.ac.in The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1207.1947 or http://arXiv.org/abs/1207.1947

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Abstract of a paper by Gilles Lancien and Eva Pernecka
by alspach＠math.okstate.edu 13 Jul '12

13 Jul '12

This is an announcement for the paper "Approximation properties and Schauder decompositions in Lipschitz-free spaces" by Gilles Lancien and Eva Pernecka. Abstract: We prove that the Lipschitz-free space over a doubling metric space has the bounded approximation property. We also show that the Lipschitz-free spaces over $\ell_1^N$ or $\ell_1$ have monotone finite-dimensional Schauder decompositions. Archive classification: math.FA Submitted from: gilles.lancien(a)univ-fcomte.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1207.1583 or http://arXiv.org/abs/1207.1583

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Abstract of a paper by Gustavo Garrigos, Eugenio Hernandez, and Timur Oikhberg
by alspach＠math.okstate.edu 13 Jul '12

13 Jul '12

This is an announcement for the paper "Lebesgue type inequalities for quasi-greedy bases" by Gustavo Garrigos, Eugenio Hernandez, and Timur Oikhberg. Abstract: We show that for quasi-greedy bases in real or complex Banach spaces the error of the thresholding greedy algorithm of order N is bounded by the best N- term error of approximation times a function of N which depends on the democracy functions and the quasi-greedy constant of the basis. If the basis is democratic this function is bounded by C logN. We show with two examples that this bound is attained for quasi-greedy democratic bases. Archive classification: math.FA Mathematics Subject Classification: 41A65, 41A46, 41A17 Report Number: 01 Remarks: 19 pages Submitted from: eugenio.hernandez(a)uam.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1207.0946 or http://arXiv.org/abs/1207.0946

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Abstract of a paper by Daniel Pellegrino, Juan Seoane-Sepulveda and Diana M. Serrano-Rodriguez
by alspach＠math.okstate.edu 13 Jul '12

13 Jul '12

This is an announcement for the paper "There exist multilinear Bohnenblust--Hille constants $(C_{n})_{n=1}^{\infty}$ with $\displaystyle \lim_{n\rightarrow \infty}(C_{n+1}-C_{n}) =0.$" by Daniel Pellegrino, Juan Seoane-Sepulveda and Diana M. Serrano-Rodriguez. Abstract: After almost 80 decades of dormancy, the Bohnenblust--Hille inequalities have experienced an effervescence of new results and sightly applications in the last years. The multilinear version of the Bohnenblust--Hille inequality asserts that for every positive integer $m\geq1$ there exists a sequence of positive constants $C_{m}\geq1$ such that% \[ \left( \sum\limits_{i_{1},\ldots,i_{m}=1}^{N}\left\vert U(e_{i_{^{1}}}% ,\ldots,e_{i_{m}})\right\vert ^{\frac{2m}{m+1}}\right) ^{\frac{m+1}{2m}}\leq C_{m}\sup_{z_{1},\ldots,z_{m}\in\mathbb{D}^{N}}\left\vert U(z_{1},\ldots ,z_{m})\right\vert \] for all $m$-linear forms $U:\mathbb{C}^{N}\times\cdots\times\mathbb{C}% ^{N}\rightarrow\mathbb{C}$ and positive integers $N$ (the same holds with slightly different constants for real scalars). The first estimates obtained for $C_{m}$ showed exponential growth but, only very recently, a striking new panorama emerged: the polynomial Bohnenblust--Hille inequality is hypercontractive and the multilinear Bohnenblust--Hille inequality is subexponential. Despite all recent advances, the existence of a family of constants $\left( C_{m}\right) _{m=1}^{\infty}$ so that \[ \lim_{n\rightarrow\infty}\left( C_{n+1}-C_{n}\right) =0 \] has not been proved yet. The main result of this paper proves that such constants do exist. As a consequence of this, we obtain new information on the optimal constants $\left( K_{n}\right) _{n=1}^{\infty}$ satisfying the multilinear Bohnenblust--Hille inequality. Let $\gamma$ be Euler's famous constant; for any $\varepsilon>0$, we show that \[ K_{n+1}-K_{n}\leq\left( 2\sqrt{2}-4e^{\frac{1}{2}\gamma-1}\right) n^{\log_{2}\left( 2^{-3/2}e^{1-\frac{1}{2}\gamma}\right) +\varepsilon}, \] for infinitely many $n$. Numerically, choosing a small $\varepsilon$, \[ K_{n+1}-K_{n}\leq0.8646\left( \frac{1}{n}\right) ^{0.4737}% \] for infinitely many $n.$ Archive classification: math.FA Submitted from: dmpellegrino(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1207.0124 or http://arXiv.org/abs/1207.0124

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