Banach

banach@mathdept.okstate.edu

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SUMIRFAS announcement
by Bill Johnson 01 Jul '10

01 Jul '10

1st ANNOUNCEMENT OF SUMIRFAS 2010 The Informal Regional Functional Analysis Seminar July 30 - August 1 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/conferences/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 2010 include Florent Baudier, On various geometric properties of metric spaces Ionut Chifan, Von Neumann algebras with unique group measure space Cartan subalgebras Ken Davidson, Nevanlinna-Pick interpolation and factorization of functionals Quanlei Fang, Commutators and localization on the Drury-Arveson space Kevin Beanland, Strictly singular operators between separable Banach spaces Ted Gamelin, Composition operators on uniform algebras Assaf Naor, Towards a calculus for non-linear spectral gaps Roger Smith, Close nuclear separable C$^*$-algebras Nicole Tomczak-Jaegermann, On random matrices with independent log-concave columns Joel A. Tropp, User-friendly tail bounds for sums of random matrices Michael Anshelevich (chair), Jinho Baik, and Roland Speicher are organizing a Concentration Week on "Orthogonal Polynomials in Probability Theory" for the week of July 6-10. The theme of this Concentration Week is orthogonal polynomial techniques in probability theory, especially in the study of random matrices, free probability, and multiple stochastic integrals. Baik and Speicher will give mini-courses designed to introduce non specialists to these topics. The home page for this Concentration Week is at http://www.math.tamu.edu/~manshel/OPPT/main.html Ilijas Farah and David Kerr (chair) are organizing a Concentration Week on "Set Theory and Functional Analysis" for the week of July 26-30. The broad theme will be recent applications of set theory in functional analysis, with emphasis on combinatorial phenomena and classifiability problems in operator algebras, dynamics, and Banach space theory. The program will include lecture series by Christian Rosendal, David Sherman, and Todor Tsankov. The home page for this Concentration Week is at http://www.math.tamu.edu/~kerr/concweek10/index.html 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. 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, contact Cara Barton <cara(a)math.tamu.edu>. For more information on the Workshop itself, 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 "Orthogonal Polynomials in Probability Theory", contact Michael Anshelevich <manshel(a)math.tamu.edu>. For information about the Concentration Week "Set Theory and Functional Analysis", contact David Kerr <kerr(a)math.tamu.edu>.

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Abstract of a paper by S.A. Argyros, V. Kanellopoulos, and K. Tyros
by alspach＠fourier.math.okstate.edu 07 Jun '10

07 Jun '10

This is an announcement for the paper "Spreading models in Banach space theory" by S.A. Argyros, V. Kanellopoulos, and K. Tyros. Abstract: We extend the classical Brunel-Sucheston definition of the spreading model by introducing the $\mathcal{F}$-sequences $(x_s)_{s\in\mathcal{F}}$ in a Banach space and the plegma families in $\mathcal{F}$ where $\mathcal{F}$ is a regular thin family. The new concept yields a transfinite increasing hierarchy of classes of 1-subsymmetric sequences. We explore the corresponding theory and we present examples establishing this hierarchy and illustrating the limitation of the theory. Archive classification: math.FA math.CO Remarks: vi+115 pages Submitted from: ktyros(a)central.ntua.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1006.0957 or http://arXiv.org/abs/1006.0957

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Abstract of a paper by Daniel Pellegrino and Joedson Santos
by alspach＠fourier.math.okstate.edu 07 Jun '10

07 Jun '10

This is an announcement for the paper 'A remark on the paper "A Unified Pietsch Domination Theorem"' by Daniel Pellegrino and Joedson Santos. Abstract: In this short communication we show that the Unified Pietsch Domination proved by Botelho et al in a recent paper remains true even if we remove two of its apparently crucial hypothesis. Archive classification: math.FA Remarks: 3 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/1006.0753 or http://arXiv.org/abs/1006.0753

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Abstract of a paper by Daniel Pellegrino
by alspach＠fourier.math.okstate.edu 07 Jun '10

07 Jun '10

This is an announcement for the paper "An inclusion principle for general classes of nonlinear absolutely summing maps" by Daniel Pellegrino. Abstract: The inclusion theorem for absolutely summing linear operators asserts that under certain assumptions on $p_{1},p_{2},q_{1}$ and $q_{2},$ every absolutely $(q_{1},p_{1})$-summing linear operator is also absolutely $(q_{2},p_{2}% )$-summing. In this note we obtain some variants of this result in a completely nonlinear setting. Archive classification: math.FA Remarks: 11 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/1006.0536 or http://arXiv.org/abs/1006.0536

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Abstract of a paper by Turdebek N. Bekjan, Zeqian Chen, and Peide Liu
by alspach＠fourier.math.okstate.edu 07 Jun '10

07 Jun '10

This is an announcement for the paper "Noncommutative weak Orlicz spaces and martingale inequalities" by Turdebek N. Bekjan, Zeqian Chen, and Peide Liu. Abstract: This paper is devoted to the study of noncommutative weak Orlicz spaces. Marcinkiewicz interpolation theorem is extended to include noncommutative weak Orlicz spaces as interpolation classes. In particular, we prove the Burkholder-Gundy inequality in the setting of noncommutative weak Orlicz spaces. Archive classification: math.FA Remarks: 26 pages Submitted from: zqchen(a)wipm.ac.cn The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1006.0091 or http://arXiv.org/abs/1006.0091

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Abstract of a paper by Bernardo Cascales, Ondrej F.K. Kalenda and Jiri Spurny
by alspach＠fourier.math.okstate.edu 07 Jun '10

07 Jun '10

This is an announcement for the paper "A quantitative version of James' compactness theorem" by Bernardo Cascales, Ondrej F.K. Kalenda and Jiri Spurny. Abstract: We introduce two measures of weak non-compactness $Ja_E$ and $Ja$ that quantify, via distances, the idea of boundary behind James' compactness theorem. These measures tell us, for a bounded subset $C$ of a Banach space $E$ and for given $x^*\in E^*$, how far from $E$ or $C$ one needs to go to find $x^{**}\in \overline{C}^{w^*}\subset E^{**}$ with $x^{**}(x^*)=\sup x^* (C)$. A quantitative version of James' compactness theorem is proved using $Ja_E$ and $Ja$, and in particular it yields the following result: {\it Let $C$ be a closed convex bounded subset of a Banach space $E$ and $r>0$. If there is an element $x_0^{**}$ in $\overline{C}^{w^*}$ whose distance to $C$ is greater than $r$, then there is $x^*\in E^*$ such that each $x^{**}\in\overline{C}^{w^*}$ at which $\sup x^*(C)$ is attained has distance to $E$ greater than $r/2$.} We indeed establish that $Ja_E$ and $Ja$ are equivalent to other measures of weak non-compactness studied in the literature. We also collect particular cases and examples showing when the inequalities between the different measures of weak non-compactness can be equalities and when the inequalities are sharp. Archive classification: math.FA Remarks: 16 pages Submitted from: kalenda(a)karlin.mff.cuni.cz The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1005.5693 or http://arXiv.org/abs/1005.5693

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Abstract of a paper by Antonio Aviles and Ondrej F.K. Kalenda
by alspach＠fourier.math.okstate.edu 07 Jun '10

07 Jun '10

This is an announcement for the paper "Compactness in Banach space theory - selected problems" by Antonio Aviles and Ondrej F.K. Kalenda. Abstract: We list a number of problems in several topics related to compactness in nonseparable Banach spaces. Namely, about the Hilbertian ball in its weak topology, spaces of continuous functions on Eberlein compacta, WCG Banach spaces, Valdivia compacta and Radon-Nikod\'{y}m compacta. Archive classification: math.FA math.GN Submitted from: kalenda(a)karlin.mff.cuni.cz The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1005.4303 or http://arXiv.org/abs/1005.4303

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Abstract of a paper by T. Bermudez, A. bonilla, F. Martinez-Gimenez, and A. Peris
by alspach＠fourier.math.okstate.edu 07 Jun '10

07 Jun '10

This is an announcement for the paper "Li-Yorke and distributionally chaotic operators" by T. Bermudez, A. bonilla, F. Martinez-Gimenez, and A. Peris. Abstract: We study Li-Yorke chaos and distributional chaos for operators on Banach spaces. More precisely, we characterize Li-Yorke chaos in terms of the existence of irregular vectors. Sufficient ``computable'' criteria for distributional and Li-Yorke chaos are given, together with the existence of dense scrambled sets under some additional conditions. We also obtain certain spectral properties. Finally, we show that every infinite dimensional separable Banach space admits a distributionally chaotic operator which is also hypercyclic. Archive classification: math.FA Mathematics Subject Classification: 47A16 Submitted from: tbermude(a)ull.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1005.3634 or http://arXiv.org/abs/1005.3634

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Abstract of a paper by Christina Brech and Piotr Koszmider
by alspach＠fourier.math.okstate.edu 03 Jun '10

03 Jun '10

This is an announcement for the paper "On biorthogonal systems whose functionals are finitely supported" by Christina Brech and Piotr Koszmider. Abstract: We show that for each natural $n>1$ it is consistent that there is a compact Hausdorff space $K_{2n}$ such that in $C(K_{2n})$ there is no uncountable (semi)biorthogonal sequence $(f_\xi,\mu_\xi)_{\xi\in \omega_1}$ where $\mu_\xi$'s are atomic measures with supports consisting of at most $2n-1$ points of $K_{2n}$, but there are biorthogonal systems $(f_\xi,\mu_\xi)_{\xi\in \omega_1}$ where $\mu_\xi$'s are atomic measures with supports consisting of $2n$ points. This complements a result of Todorcevic that it is consistent that each nonseparable Banach space $C(K)$ has an uncountable biorthogonal system where the functionals are measures of the form $\delta_{x_\xi}-\delta_{y_\xi}$ for $\xi<\omega_1$ and $x_\xi,y_\xi\in K$. It also follows that it is consistent that the irredundance of the Boolean algebra $Clop(K)$ or the Banach algebra $C(K)$ for $K$ totally disconnected can be strictly smaller than the sizes of biorthogonal systems in $C(K)$. The compact spaces exhibit an interesting behaviour with respect to known cardinal functions: the hereditary density of the powers $K_{2n}^k$ is countable up to $k=n$ and it is uncountable (even the spread is uncountable) for $k>n$. Archive classification: math.FA Submitted from: christina.brech(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1005.3532 or http://arXiv.org/abs/1005.3532

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Abstract of a paper by Christina Brech and Piotr Koszmider
by alspach＠fourier.math.okstate.edu 03 Jun '10

03 Jun '10

This is an announcement for the paper "On universal Banach spaces of density continuum" by Christina Brech and Piotr Koszmider. Abstract: We consider the question whether there exists a Banach space $X$ of density continuum such that every Banach space of density not bigger than continuum isomorphically embeds into $X$ (called a universal Banach space of density $\cc$). It is well known that $\ell_\infty/c_0$ is such a space if we assume the continuum hypothesis. However, some additional set-theoretic assumption is needed, as we prove in the main result of this paper that it is consistent with the usual axioms of set-theory that there is no universal Banach space of density $\cc$. Thus, the problem of the existence of a universal Banach space of density $\cc$ is undecidable using the usual axioms of set-theory. We also prove that it is consistent that there are universal Banach spaces of density $\cc$, but $\ell_\infty/c_0$ is not among them. This relies on the proof of the consistency of the nonexistence of an isomorphic embedding of $C([0,\cc])$ into $\ell_\infty/c_0$. Archive classification: math.FA Submitted from: christina.brech(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1005.3530 or http://arXiv.org/abs/1005.3530

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