Banach July 2013

banach@mathdept.okstate.edu

2 participants
17 discussions

INFORMAL ANALYSIS SEMINAR DEDICATED TO THE WORK OF JOE DIESTEL (March 20-21, 2010)
by Artem Zvavitch 20 Aug '16

20 Aug '16

Dear Friends, On Saturday - Sunday, March 20-21, 2010, (best arrival date Friday, March 19/ Departure Monday, March 22) the Department of Mathematical Sciences at Kent State University will be famous but still very informal. We are happy to announce an: INFORMAL ANALYSIS SEMINAR DEDICATED TO THE WORK OF JOE DIESTEL The following people are among speakers: Peter Casazza, Hans Jarchow, Alexander Koldobsky, Pepe Orihuela, Olek Pelczynski, Thomas Schlumprecht, Lutz Weis. It would be great if you could visit Kent State and participate in the seminar! The conference will have a registration fee of $200 WHICH INCLUDES: pick up/drop off from the airport, THREE DAY STAY in the Microtel hotel at Streetsboro, Saturday/Sunday lunches/dinners to be provided at the department. If you plan to stay fewer than 3 nights or prefer to make your own accommodation arrangements, please reduce your registration fee by $45 per day that you will not use our hotel arrangements. If possible, please send a check for your registration fee, made out to the Department of Mathematical Sciences, Kent State University. The check should be mailed to Virginia Wright, Department of Mathematical Sciences, Kent State University, Kent, OH, 44242. The fee can be also be paid during the registration (check/cash). The conference is supported by NSF; The Department of Mathematical Sciences and Kent State University. Depending on funds availability the fee may be waived for young researchers and people without available funding. Please, write as soon as possible to zvavitch(a)math.kent.edu May we ask you to respond as soon as February 19 (zvavitch(a)math.kent.edu), so that we can gauge the need for housing, lecture room(s), etc. Best Regards, Analysis group at Kent State!

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Abstract of a paper by Manuel D. Contreras, Santiago Diaz-Madrigal, and Dragan Vukotic
by alspach＠math.okstate.edu 26 Jul '13

26 Jul '13

This is an announcement for the paper "Compact and weakly compact composition operators from the Bloch space into M\"obius invariant spaces" by Manuel D. Contreras, Santiago Diaz-Madrigal, and Dragan Vukotic. Abstract: We obtain exhaustive results and treat in a unified way the question of boundedness, compactness, and weak compactness of composition operators from the Bloch space into any space from a large family of conformally invariant spaces that includes the classical spaces like $BMOA$, $Q_\alpha$, and analytic Besov spaces $B^p$. In particular, by combining techniques from both complex and functional analysis, we prove that in this setting weak compactness is equivalent to compactness. For the operators into the corresponding ``small'' spaces we also characterize the boundedness and show that it is equivalent to compactness. Archive classification: math.FA Mathematics Subject Classification: 47B33 Submitted from: dragan.vukotic(a)uam.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1307.5784 or http://arXiv.org/abs/1307.5784

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Abstract of a paper by Umut Caglar and Elisabeth M. Werner
by alspach＠math.okstate.edu 26 Jul '13

26 Jul '13

This is an announcement for the paper "Divergence for s-concave and log concave functions" by Umut Caglar and Elisabeth M. Werner. Abstract: We prove new entropy inequalities for log concave and s-concave functions that strengthen and generalize recently established reverse log Sobolev and Poincare inequalities for such functions. This leads naturally to the concept of f-divergence and, in particular, relative entropy for s-concave and log concave functions. We establish their basic properties, among them the affine invariant valuation property. Applications are given in the theory of convex bodies. Archive classification: math.FA 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/1307.5409 or http://arXiv.org/abs/1307.5409

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Abstract of a paper by Daniel Pellegrino and Juan B. Seoane-Sepulveda
by alspach＠math.okstate.edu 26 Jul '13

26 Jul '13

This is an announcement for the paper "Grothendieck's theorem for absolutely summing multilinear operators is optimal" by Daniel Pellegrino and Juan B. Seoane-Sepulveda. Abstract: Grothendieck's theorem asserts that every continuous linear operator from $\ell_{1}$ to $\ell_{2}$ is absolutely $\left( 1;1\right) $-summing. In this note we prove that the optimal constant $g_{m}$ so that every continuous $m$-linear operator from $\ell_{1}\times\cdots\times\ell_{1}$ to $\ell_{2}$ is absolutely $\left(g_{m};1\right) $-summing is $\frac{2}{m+1}$. This result solves (in the positive) a conjecture posed by A.T. Bernardino in 2011. Archive classification: math.FA Submitted from: pellegrino(a)pq.cnpq.br The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1307.4809 or http://arXiv.org/abs/1307.4809

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Abstract of a paper by Antonio Aviles, Felix Cabello Sanchez, Jesus M. F. Castillo, Manuel Gonzalez and Yolanda Moreno
by alspach＠math.okstate.edu 26 Jul '13

26 Jul '13

This is an announcement for the paper "On ultrapowers of Banach spaces of type $\mathscr L_\infty$" by Antonio Aviles, Felix Cabello Sanchez, Jesus M. F. Castillo, Manuel Gonzalez and Yolanda Moreno. Abstract: We prove that no ultraproduct of Banach spaces via a countably incomplete ultrafilter can contain $c_0$ complemented. This shows that a ``result'' widely used in the theory of ultraproducts is wrong. We then amend a number of results whose proofs had been infected by that statement. In particular we provide proofs for the following statements: (i) All $M$-spaces, in particular all $C(K)$-spaces, have ultrapowers isomorphic to ultrapowers of $c_0$, as well as all their complemented subspaces isomorphic to their square. (ii) No ultrapower of the Gurari\u \i\ space can be complemented in any $M$-space. (iii) There exist Banach spaces not complemented in any $C(K)$-space having ultrapowers isomorphic to a $C(K)$-space. Archive classification: math.FA Remarks: This paper is to appear in Fundamenta Mathematica Submitted from: castillo(a)unex.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1307.4387 or http://arXiv.org/abs/1307.4387

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Abstract of a paper by Jesus M. F. Castillo, Valentin Ferenczi and Yolanda Moreno
by alspach＠math.okstate.edu 26 Jul '13

26 Jul '13

This is an announcement for the paper "On uniformly finitely extensible Banach spaces" by Jesus M. F. Castillo, Valentin Ferenczi and Yolanda Moreno. Abstract: We continue the study of Uniformly Finitely Extensible Banach spaces (in short, UFO) initiated in Moreno-Plichko, \emph{On automorphic Banach spaces}, Israel J. Math. 169 (2009) 29--45 and Castillo-Plichko, \emph{Banach spaces in various positions.} J. Funct. Anal. 259 (2010) 2098-2138. We show that they have the Uniform Approximation Property of Pe\l czy\'nski and Rosenthal and are compactly extensible. We will also consider their connection with the automorphic space problem of Lindenstrauss and Rosenthal --do there exist automorphic spaces other than $c_0(I)$ and $\ell_2(I)$?-- showing that a space all whose subspaces are UFO must be automorphic when it is Hereditarily Indecomposable (HI), and a Hilbert space when it is either locally minimal or isomorphic to its square. We will finally show that most HI --among them, the super-reflexive HI space constructed by Ferenczi-- and asymptotically $\ell_2$ spaces in the literature cannot be automorphic. Archive classification: math.FA Remarks: This paper is to appear in the Journal of Mathematical Analysis and The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1307.4386 or http://arXiv.org/abs/1307.4386

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Abstract of a paper by Jesus M. F. Castillo, Pier Luigi Papini and Marilda A. Simoes
by alspach＠math.okstate.edu 26 Jul '13

26 Jul '13

This is an announcement for the paper "Thick coverings for the unit ball of a Banach space" by Jesus M. F. Castillo, Pier Luigi Papini and Marilda A. Simoes. Abstract: We study the behaviour of Whitley's thickness constant of a Banach space with respect to $\ell_p$-products and we compute it for classical $L_p$-spaces. Archive classification: math.FA Remarks: This paper is to appear in Houston Journal of Mathematics Submitted from: castillo(a)unex.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1307.4385 or http://arXiv.org/abs/1307.4385

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Abstract of a paper by Jesus M.F. Castillo, and Yolanda Moreno
by alspach＠math.okstate.edu 26 Jul '13

26 Jul '13

This is an announcement for the paper "On the bounded approximation property in Banach spaces" by Jesus M.F. Castillo, and Yolanda Moreno. Abstract: We prove that the kernel of a quotient operator from an $\mathcal L_1$-space onto a Banach space $X$ with the Bounded Approximation Property (BAP) has the BAP. This completes earlier results of Lusky --case $\ell_1$-- and Figiel, Johnson and Pe\l czy\'nski --case $X^*$ separable. Given a Banach space $X$, we show that if the kernel of a quotient map from some $\mathcal L_1$-space onto $X$ has the BAP then every kernel of every quotient map from any $\mathcal L_1$-space onto $X$ has the BAP. The dual result for $\mathcal L_\infty$-spaces also hold: if for some $\mathcal L_\infty$-space $E$ some quotient $E/X$ has the BAP then for every $\mathcal L_\infty$-space $E$ every quotient $E/X$ has the BAP. Archive classification: math.FA Remarks: To appear in Israel Journal of Mathematics Submitted from: castillo(a)unex.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1307.4383 or http://arXiv.org/abs/1307.4383

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Abstract of a paper by Jesus M. F. Castillo and Felix Cabello Sanchez
by alspach＠math.okstate.edu 26 Jul '13

26 Jul '13

This is an announcement for the paper "Stability constants and the homology of quasi-Banach spaces" by Jesus M. F. Castillo and Felix Cabello Sanchez. Abstract: We affirmatively solve the main problems posed by Laczkovich and Paulin in \emph{Stability constants in linear spaces}, Constructive Approximation 34 (2011) 89--106 (do there exist cases in which the second Whitney constant is finite while the approximation constant is infinite?) and by Cabello and Castillo in \emph{The long homology sequence for quasi-Banach spaces, with applications}, Positivity 8 (2004) 379--394 (do there exist Banach spaces $X,Y$ for which $\Ext(X,Y)$ is Hausdorff and non-zero?). In fact, we show that these two problems are the same. Archive classification: math.FA Remarks: This paper is to appear in Israel Journal of Mathematics Submitted from: castillo(a)unex.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1307.4382 or http://arXiv.org/abs/1307.4382

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Abstract of a paper by Simon Lucking
by alspach＠math.okstate.edu 26 Jul '13

26 Jul '13

This is an announcement for the paper "The almost Daugavet property and translation-invariant subspaces" by Simon Lucking. Abstract: Let $G$ be a metrizable, compact abelian group and let $\Lambda$ be a subset of its dual group $\widehat G$. We show that $C_\Lambda(G)$ has the almost Daugavet property if and only if $\Lambda$ is an infinite set, and that $L^1_\Lambda(G)$ has the almost Daugavet property if and only if $\Lambda$ is not a $\Lambda(1)$ set. Archive classification: math.FA Mathematics Subject Classification: 46B04, 43A46 Remarks: 12 pages Submitted from: simon.luecking(a)fu-berlin.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1307.3629 or http://arXiv.org/abs/1307.3629

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Banach July 2013