Banach July 2012

banach@mathdept.okstate.edu

3 participants
26 discussions

Abstract of a paper by Szymon Glab, Pedro L. Kaufmann and Leonardo Pellegrini
by alspach＠math.okstate.edu 26 Jul '12

26 Jul '12

This is an announcement for the paper "Large structures made of nowhere $L^p$ functions" by Szymon Glab, Pedro L. Kaufmann and Leonardo Pellegrini. Abstract: We say that a real-valued function $f$ defined on a positive Borel measure space $(X,\mu)$ is nowhere $q$-integrable if, for each nonvoid open subset $U$ of $X$, the restriction $f|_U$ is not in $L^q(U)$. When $X$ is a Polish space and $\mu$ satisfies some natural properties, we show that certain sets of functions which are $p$-integrable for some $p$'s but nowhere $q$-integrable for some other $q$'s ($0<p,q<\infty$) admit large linear and algebraic structures within them. In our Polish space context, the presented results answer a question from Bernal-Gonz\'alez [L. Bernal-Gonz\'alez, Algebraic genericity and strict-order integrability, Studia Math. 199(3)(2010), 279--293], and improves and complements results of several authors. Archive classification: math.FA Submitted from: leoime(a)yahoo.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1207.3818 or http://arXiv.org/abs/1207.3818

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Abstract of a paper by Christian Rosendal
by alspach＠math.okstate.edu 26 Jul '12

26 Jul '12

This is an announcement for the paper "Rigidity of commuting affine actions on reflexive Banach spaces" by Christian Rosendal. Abstract: We give a simple argument to show that if {\alpha} is an afﬁne isometric action of a product G x H of topological groups on a reﬂexive Banach space X with linear part {\pi}, then either {\pi}(H) ﬁxes a unit vector or {\alpha}|G almost ﬁxes a point on X. It follows that any afﬁne isometric action of an abelian group on a reﬂexive Banach space X, whose linear part ﬁxes no unit vectors, almost ﬁxes points on X. Archive classification: math.GR math.FA Submitted from: rosendal.math(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1207.3731 or http://arXiv.org/abs/1207.3731

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Abstract of a paper by Mikolaj Krupski and Witold Marciszewski
by alspach＠math.okstate.edu 26 Jul '12

26 Jul '12

This is an announcement for the paper "Some remarks on universality properties of $\ell_\infty / c_0$" by Mikolaj Krupski and Witold Marciszewski. Abstract: We prove that if continuum is not a Kunen cardinal, then there is a uniform Eberlein compact space $K$ such that the Banach space $C(K)$ does not embed isometrically into $\ell_\infty/c_0$. We prove a similar result for isomorphic embeddings. We also construct a consistent example of a uniform Eberlein compactum whose space of continuous functions embeds isomorphically into $\ell_\infty/c_0$, but fails to embed isometrically. As far as we know it is the first example of this kind. Archive classification: math.FA Mathematics Subject Classification: Primary 46B26, 46E15, Secondary 03E75 Submitted from: krupski(a)impan.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1207.3722 or http://arXiv.org/abs/1207.3722

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Abstract of a paper by Anil Kumar Karn and Deba Prasad Sinha
by alspach＠math.okstate.edu 26 Jul '12

26 Jul '12

This is an announcement for the paper "An operator summability of sequences in Banach spaces" by Anil Kumar Karn and Deba Prasad Sinha. Abstract: Let $1 \leq p <\infty$. A sequence $\lef x_n \rig$ in a Banach space $X$ is defined to be $p$-operator summable if for each $\lef f_n \rig \in l^{w^*}_p(X^*)$, we have $\lef \lef f_n(x_k)\rig _k \rig _n \in l^s_p(l_p)$. Every norm $p$-summable sequence in a Banach space is operator $p$-summable, while in its turn every operator $p$-summable sequence is weakly $p$-summable. An operator $T \in B(X, Y)$ is said to be $p$-limited if for every $\lef x_n \rig \in l_p^w(X)$, $\lef Tx_n \rig$ is operator $p$-summable. The set of all $p$-limited operators form a normed operator ideal. It is shown that every weakly $p$-summable sequence in $X$ is operator $p$-summable if and only if every operator $T \in B(X, l_p)$ is $p$-absolutely summing. On the other hand every operator $p$-summable sequence in $X$ is norm $p$-summable if and only if every $p$-limited operator in $B(l_{p'}, X)$ is absolutely $p$-summing. Moreover, this is the case if and only if $X$ is a subspace of $L_p(\mu )$ for some Borel measure $\mu$. Archive classification: math.FA Mathematics Subject Classification: Primary 46B20, Secondary 46B28, 46B50 Remarks: 16 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/1207.3620 or http://arXiv.org/abs/1207.3620

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Abstract of a paper by Tomasz Kochanek
by alspach＠math.okstate.edu 26 Jul '12

26 Jul '12

This is an announcement for the paper "$\mathcal F$-bases with individual brackets in Banach spaces" by Tomasz Kochanek. Abstract: We provide a partial answer to the question of Vladimir Kadets whether given an $\mathcal F$-basis of a~Banach space $X$, with respect to some filter $\mathcal F\subset \mathcal P(\mathbb N)$, the coordinate functionals are continuous. The answer is positive if the character of $\mathcal F$ is less than $\mathfrak{p}$. In this case every $\mathcal F$-basis with individual brackets is an $M$-basis with brackets determined by a set from $\mathcal F$. Archive classification: math.FA Submitted from: t.kania(a)lancaster.ac.uk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1207.3097 or http://arXiv.org/abs/1207.3097

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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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Banach July 2012