Banach

banach@mathdept.okstate.edu

2549 discussions

Abstract of a paper by Spiros A. Argyros, A. Manoussakis, and Anna M. Pelczar
by alspach＠fourier.math.okstate.edu 17 Aug '09

17 Aug '09

This is an announcement for the paper "On the hereditary proximity to $\ell_1$" by Spiros A. Argyros, A. Manoussakis, and Anna M. Pelczar. Abstract: In the first part of the paper we present and discuss concepts of local and asymptotic hereditary proximity to \ell_1. The second part is devoted to a complete separation of the hereditary local proximity to \ell_1 from the asymptotic one. More precisely for every countable ordinal \xi we construct a separable reflexive space \mathfrak{X}_\xi such that every infinite dimensional subspace of it has Bourgain \ell_1-index greater than \omega^\xi and the space itself has no \ell_1-spreading model. We also present a reflexive HI space admitting no \ell_p as a spreading model. Archive classification: math.FA Mathematics Subject Classification: 46B20; 46B15; 03E10; 05A17 Remarks: 40 pages, submitted for publication The source file(s), proximity.tex: 158273 bytes, is(are) stored in gzipped form as 0907.4317.gz with size 43kb. The corresponding postcript file has gzipped size 238kb. Submitted from: anna.pelczar(a)im.uj.edu.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0907.4317 or http://arXiv.org/abs/0907.4317 or by email in unzipped form by transmitting an empty message with subject line uget 0907.4317 or in gzipped form by using subject line get 0907.4317 to: math(a)arXiv.org.

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Abstract of a paper by Dario Cordero-Erausquin and Michel Ledoux
by alspach＠fourier.math.okstate.edu 17 Aug '09

17 Aug '09

This is an announcement for the paper "The geometry of Euclidean convolution inequalities and entropy" by Dario Cordero-Erausquin and Michel Ledoux. Abstract: The goal of this note is to show that some convolution type inequalities from Harmonic Analysis and Information Theory, such as Young's convolution inequality (with sharp constant), Nelson's hypercontractivity of the Hermite semi-group or Shannon's inequality, can be reduced to a simple geometric study of frames of $\R^2$. We shall derive directly entropic inequalities, which were recently proved to be dual to the Brascamp-Lieb convolution type inequalities. Archive classification: math.FA math.PR The source file(s), geoconv5.tex: 49291 bytes, is(are) stored in gzipped form as 0907.2861.gz with size 16kb. The corresponding postcript file has gzipped size 113kb. Submitted from: cordero(a)math.jussieu.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0907.2861 or http://arXiv.org/abs/0907.2861 or by email in unzipped form by transmitting an empty message with subject line uget 0907.2861 or in gzipped form by using subject line get 0907.2861 to: math(a)arXiv.org.

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2009 SUMIRFAS schedule
by Dale Alspach 27 Jul '09

27 Jul '09

The schedule can be found here http://www.math.okstate.edu/~alspach/banach/IRFASschedule09.pdf Dale Alspach

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2009 SUMIRFAS schedule
by Bill Johnson 27 Jul '09

27 Jul '09

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Abstract of a paper by V.Capraro and S.Rossi
by alspach＠fourier.math.okstate.edu 14 Jul '09

14 Jul '09

This is an announcement for the paper "Banach spaces which embed into their dual" by V.Capraro and S.Rossi. Abstract: We provide a nice characterization of the classical Riesz-Frechet representation theorem: if a Banach space embeds isometrically into its dual space, under some other natural assumptions, then it is a Hilbert space and the embedding is actually the canonical one (which becomes automatically surjective). We also see that requiring surjectivity a priori, one can considerably weak one of the ''other hypothesis''. Anyway, it should remains to prove that our assumptions are minimal. It seems to be a difficult problem in general, because it is already not easy at all to find non-trivial examples (Hilbert spaces!) of Banach spaces which embed isometrically into their own dual. We will discuss in some details only the fatality of the ''isometric hypothesi'' which however brought us to find an example of compact convex Hausdorff space which does not admit a Borel measure with full support. Archive classification: math.FA Remarks: 7 pages The source file(s), articolo.tex: 17079 bytes, is(are) stored in gzipped form as 0907.1813.gz with size 6kb. The corresponding postcript file has gzipped size 50kb. Submitted from: capraro(a)mat.uniroma2.it The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0907.1813 or http://arXiv.org/abs/0907.1813 or by email in unzipped form by transmitting an empty message with subject line uget 0907.1813 or in gzipped form by using subject line get 0907.1813 to: math(a)arXiv.org.

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Abstract of a paper by Sean Dineen and Richard M. Timoney
by alspach＠fourier.math.okstate.edu 14 Jul '09

14 Jul '09

This is an announcement for the paper "Complex geodesics on convex domains" by Sean Dineen and Richard M. Timoney. Abstract: Existence and uniqueness of complex geodesics joining two points of a convex bounded domain in a Banach space $X$ are considered. Existence is proved for the unit ball of $X$ under the assumption that $X$ is 1-complemented in its double dual. Another existence result for taut domains is also proved. Uniqueness is proved for strictly convex bounded domains in spaces with the analytic Radon-Nikodym property. If the unit ball of $X$ has a modulus of complex uniform convexity with power type decay at 0, then all complex geodesics in the unit ball satisfy a Lipschitz condition. The results are applied to classical Banach spaces and to give a formula describing all complex geodesics in the unit ball of the sequence spaces $\ell^p$ ($1 \leq p < \infty$). Archive classification: math.FA math.CV math.MG Mathematics Subject Classification: 46G20; 32H15; 46B45; 53C22 Citation: Progress in Functional Analysis, North Holland Mathematical The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0907.1194 or http://arXiv.org/abs/0907.1194 or by email in unzipped form by transmitting an empty message with subject line uget 0907.1194 or in gzipped form by using subject line get 0907.1194 to: math(a)arXiv.org.

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Abstract of a paper by R. Fry and L. Keener
by alspach＠fourier.math.okstate.edu 14 Jul '09

14 Jul '09

This is an announcement for the paper "Corrigendum to [Approximation by Lipschitz, C^{p} smooth functions on weakly compactly generated Banach spaces, J. Funct. Anal. 252 (2007), no. 1, 34--41.]" by R. Fry and L. Keener. Abstract: This note is a corrigendum to an earlier paper by the first named author. The original proof contained a gap which is here corrected under the formally stronger hypothesis that X admit a C^{p} smooth norm rather than merely a Lipschitz, C^{p} smooth bump function. More precisely, it is shown that on weakly compactly generated Banach spaces X which admit a C^{p} smooth norm, one can uniformly approximate uniformly continuous functions f:X->R by Lipschitz, C^{p} smooth functions. Additionally it is shown in this note that there is a constant C>1 so that any L-Lipschitz function f:X->R can be uniformly approximated by CL-Lipschitz, C^{p} smooth functions. This provides a `Lipschitz version' of the classical approximation results of Godefroy, Troyanski, Whitfield and Zizler. Archive classification: math.FA Mathematics Subject Classification: 46B20 The source file(s), LIPWCGJune3009.tex: 45249 bytes, is(are) stored in gzipped form as 0907.0241.gz with size 12kb. The corresponding postcript file has gzipped size 98kb. Submitted from: rfry(a)tru.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0907.0241 or http://arXiv.org/abs/0907.0241 or by email in unzipped form by transmitting an empty message with subject line uget 0907.0241 or in gzipped form by using subject line get 0907.0241 to: math(a)arXiv.org.

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Abstract of a paper by Marius Junge and Quanhua Xu
by alspach＠fourier.math.okstate.edu 14 Jul '09

14 Jul '09

This is an announcement for the paper "Representation of certain homogeneous Hilbertian operator spaces and applications" by Marius Junge and Quanhua Xu. Abstract: Following Grothendieck's characterization of Hilbert spaces we consider operator spaces $F$ such that both $F$ and $F^*$ completely embed into the dual of a C*-algebra. Due to Haagerup/Musat's improved version of Pisier/Shlyakhtenko's Grothendieck inequality for operator spaces, these spaces are quotients of subspaces of the direct sum $C\oplus R$ of the column and row spaces (the corresponding class being denoted by $QS(C\oplus R)$). We first prove a representation theorem for homogeneous $F\in QS(C\oplus R)$ starting from the fundamental sequences defined by column and row norms of unit vectors. Under a mild regularity assumption on these sequences we show that they completely determine the operator space structure of $F$ and find a canonical representation of this important class of homogeneous Hilbertian operator spaces in terms of weighted row and column spaces. This canonical representation allows us to get an explicit formula for the exactness constant of an $n$-dimensional subspace $F_n$ of $F$ involving the fundamental sequences. Similarly, we have formulas for the the projection (=injectivity) constant of $F_n$. They also permit us to determine the completely 1-summing maps in Effros and Ruan's sense between two homogeneous spaces $E$ and $F$ in $QS(C\oplus R)$. Archive classification: math.FA math.OA Mathematics Subject Classification: 46L07; 47L25 Remarks: To appear in Invent. Math The source file(s), orlicz.tex: 131749 bytes, is(are) stored in gzipped form as 0906.5308.gz with size 39kb. The corresponding postcript file has gzipped size 223kb. Submitted from: quanhua.xu(a)univ-fcomte.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0906.5308 or http://arXiv.org/abs/0906.5308 or by email in unzipped form by transmitting an empty message with subject line uget 0906.5308 or in gzipped form by using subject line get 0906.5308 to: math(a)arXiv.org.

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Abstract of a paper by Eric Ricard and Quanhua Xu
by alspach＠fourier.math.okstate.edu 14 Jul '09

14 Jul '09

This is an announcement for the paper "Complex interpolation of weighted noncommutative $L_p$-spaces" by Eric Ricard and Quanhua Xu. Abstract: Let $\mathcal{M}$ be a semifinite von Neumann algebra equipped with a semifinite normal faithful trace $\tau$. Let $d$ be an injective positive measurable operator with respect to $(\mathcal{M},\,\tau)$ such that $d^{-1}$ is also measurable. Define $$L_p(d)=\left\{x\in L_0(\mathcal{M})\;:\; dx+xd\in L_p(\mathcal{M})\right\}\quad\mbox{and}\quad \|x\|_{L_p(d)}=\|dx+xd\|_p\,.$$ We show that for $1\le p_0<p_1\le\8$, $0<\theta<1$ and $\alpha_0\ge0, \alpha_1\ge0$ the interpolation equality $$(L_{p_0}(d^{\alpha_0}),\;L_{p_1}(d^{\alpha_1}))_\theta =L_{p}(d^{\alpha})$$ holds with equivalent norms, where $\frac1p=\frac{1-\theta}{p_0}+\frac{\theta}{p_1}$ and $\alpha=(1-\theta)\alpha_0+\theta\alpha_1$. Archive classification: math.FA math.OA Mathematics Subject Classification: 46L50; 46M35; 47L15 Remarks: To appear in Houston J. Math The source file(s), inter.tex: 37005 bytes, is(are) stored in gzipped form as 0906.5305.gz with size 12kb. The corresponding postcript file has gzipped size 90kb. Submitted from: quanhua.xu(a)univ-fcomte.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0906.5305 or http://arXiv.org/abs/0906.5305 or by email in unzipped form by transmitting an empty message with subject line uget 0906.5305 or in gzipped form by using subject line get 0906.5305 to: math(a)arXiv.org.

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SUMIRFAS 2009
by Bill Johnson 13 Jul '09

13 Jul '09

1st ANNOUNCEMENT OF SUMIRFAS 2009 The Informal Regional Functional Analysis Seminar August 7 - 9 Texas A&M University, College Station Schedule: Talks for SUMIRFAS will be posted on the Workshop in Analysis and Probability page, URL http://www.math.tamu.edu/research/workshops/linanalysis/ 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.tamu.edu/map/building/overview/BLOC.html. Coffee and refreshments will be available in Blocker 148. Speakers at SUMIRFAS 2009 include Lewis Bowen, Orbit equivalence flexibility Dorin Dutkay, Fourier series on fractals Daniel Freeman, The universality of ell_1 as a dual space Maria Girardi, Operator-valued martingale transforms and applications Richard Haydon, TBA Peter Kuchment, TBA Hangfen Li, Convex analysis and noncommutative Choquet boundary Mikhail Ostrovskii, Unitarizable representations and fixed points of groups of biholomorphic transformations of operator balls Mihai Popa, On the conditionally free analogue of the S-transform Sorin Popa, Group measure space decomposition of factors and W*-superrigidity Rachel Ward, Quiet sigma delta quantization: removing noisy periodicities in analog-to-digital conversion Rafal Latala, Assaf Naor, and Grigoris Paouris (chair) are organizing a Concentration Week on "Probability in Asymptotic Geometry" for the week of July 20-24. This Concentration Week will focus on high dimensional phenomena concerning convex bodies, random polytopes, and random matrices. These topics lie in the intersection of probability, analysis, geometry, and combinatorics. The goal is to expose the huge variety of techniques used in the study of these objects and to explore the connections between them. Marius Junge, Jesse Peterson, and Gilles Pisier (chair) are organizing a Concentration Week on "Operator Spaces and Approximation Properties of Discrete Groups" for the week of August 3-7. Particular emphasis will be taken to tie together recent results from the theory of von Neumann algebras with operator space ideas. The intention is to provide a background for common points of interest from different perspectives through courses on operator spaces and Dirichlet forms in von Neumann algebras. The intention of this concentration week is to attract attention of younger researchers and students to these new openings. We expect to be able to cover housing for most participants from support the National Science Foundation has provided for the Workshop. Preference will be given to participants who do not have other sources of support, such as sponsored research grants. When you ask Cara to book your room, please tell her if you are requesting support. Minorities, women, graduate students, and young researchers are especially encouraged to apply. 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 Larson <larson(a)math.tamu.edu>, Gilles Pisier <pisier(a)math.tamu.edu>, or Joel Zinn <jzinn(a)math.tamu.edu>. For information about the Concentration Week "Probability in Asymptotic Geometry" contact Grigoris Paouris <grigoris(a)math.tamu.edu>. For information about the Concentration Week on "Operator Spaces and Approximation Properties of Discrete Groups", contact Gilles Pisier <pisier(a)math.tamu.edu>.

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