June 2015 - Banach - mathdept.okstate.edu

Abstract of a paper by Pablo Turco
by alspach＠math.okstate.edu 11 Jun '15

11 Jun '15

This is an announcement for the paper "$\mathcal A$-compact mappings" by Pablo Turco. Abstract: For a fixed Banach operator ideal $\mathcal A$, we study $\mathcal A$-compact polynomials and $\mathcal A$-compact holomorphic mappings. We show that the behavior of $\mathcal A$-compact polynomials is determined by its behavior in any neighborhood of any point. We transfer some known properties of $\mathcal A$-compact operators to $\mathcal A$-compact polynomials. In order to study $\mathcal A$-compact holomorphic functions, we appeal to the $\mathcal A$-compact radius of convergence which allows us to characterize the functions in this class. Under certain hypothesis on the ideal $\mathcal A$, we give examples showing that our characterization is sharp. Archive classification: math.FA Mathematics Subject Classification: 46G20, 46B20, 46G25 Remarks: 21 Pages Submitted from: paturco(a)dm.uba.ar The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1505.08037 or http://arXiv.org/abs/1505.08037

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Abstract of a paper by Marek Cuth and Marian Fabian
by alspach＠math.okstate.edu 11 Jun '15

11 Jun '15

This is an announcement for the paper "Separable reduction of Frechet subdifferentiability in Asplund spaces" by Marek Cuth and Marian Fabian. Abstract: In the framework of Asplund spaces, we use two equivalent instruments - rich families and suitable models from logic - for performing separable reductions of various statements on Frechet subdifferentiability of functions. This way, isometrical results are actually obtained and several existed proofs are substantially simplified. Everything is based on a new structural characterization of Asplund spaces. Archive classification: math.FA Mathematics Subject Classification: 46B26, 58C20, 46B20, 03C30 Submitted from: marek.cuth(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1505.07604 or http://arXiv.org/abs/1505.07604

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Abstract of a paper by Marek Cuth, Michal Doucha, and Przemyslaw Wojtaszczyk
by alspach＠math.okstate.edu 11 Jun '15

11 Jun '15

This is an announcement for the paper "On the structure of Lipschitz-free spaces" by Marek Cuth, Michal Doucha, and Przemyslaw Wojtaszczyk. Abstract: In this note we study the structure of Lipschitz-free Banach spaces. We show that every Lipschitz-free Banach space contains a complemented copy of $\ell_1$. This result has many consequences for the structure of Lipschitz-free Banach spaces. Moreover, we give an example of a countable compact metric space $K$ such that $F(K)$ is not isomorphic to a subspace of $L_1$ and we show that whenever $M$ is a subset of $R^n$, then $F(M)$ is weakly sequentially complete; in particular, $c_0$ does not embed into $F(M)$. Archive classification: math.FA Mathematics Subject Classification: 46B03, 54E35 Submitted from: marek.cuth(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1505.07209 or http://arXiv.org/abs/1505.07209

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Abstract of a paper by Claudia Correa and Daniel V. Tausk
by alspach＠math.okstate.edu 11 Jun '15

11 Jun '15

This is an announcement for the paper "Nontrivial twisted sums of $c_0$ and $C(K)$" by Claudia Correa and Daniel V. Tausk. Abstract: We obtain a new large class of compact Hausdorff spaces $K$ for which $c_0$ can be nontrivially twisted with $C(K)$. Archive classification: math.FA Mathematics Subject Classification: 46B20, 46E15 Remarks: 10 pages Submitted from: tausk(a)ime.usp.br The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1505.06727 or http://arXiv.org/abs/1505.06727

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Abstract of a paper by E. Ostrovsky and L. Sirota
by alspach＠math.okstate.edu 11 Jun '15

11 Jun '15

This is an announcement for the paper "Strengthening of weak convergence for Radon measures in separable Banach spaces" by E. Ostrovsky and L. Sirota. Abstract: We prove in this short report that for arbitrary weak converging sequence of sigma-finite Borelian measures in the separable Banach space there is a compact embedded separable subspace such that this measures not only are concentrated in this subspace but weak converge therein. Archive classification: math.FA Submitted from: leos(a)post.sce.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1505.06235 or http://arXiv.org/abs/1505.06235

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Abstract of a paper by Henning Kempka and Jan Vybiral
by alspach＠math.okstate.edu 11 Jun '15

11 Jun '15

This is an announcement for the paper "Volumes of unit balls of mixed sequence spaces" by Henning Kempka and Jan Vybiral. Abstract: The volume of the unit ball of the Lebesgue sequence space $\ell_p^m$ is very well known since the times of Dirichlet. We calculate the volume of the unit ball in the mixed norm $\ell^n_q(\ell_p^m)$, whose special cases are nowadays popular in machine learning under the name of group lasso. We consider the real as well as the complex case. The result is given by a closed formula involving the gamma function, only slightly more complicated than the one of Dirichlet. We close by an overview of open problems. Archive classification: math.FA Submitted from: vybiral(a)karlin.mff.cuni.cz The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1505.05867 or http://arXiv.org/abs/1505.05867

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Abstract of a paper by Antonio M. Peralta and Hermann Pfitzner
by alspach＠math.okstate.edu 11 Jun '15

11 Jun '15

This is an announcement for the paper "Weak Banach-Saks property and Koml\'os' theorem for preduals of JBW$^*$-triples" by Antonio M. Peralta and Hermann Pfitzner. Abstract: We show that the predual of a JBW$^*$-triple has the weak Banach-Saks property, that is, reflexive subspaces of a JBW$^*$-triple predual are super-reflexive. We also prove that JBW$^*$-triple preduals satisfy the Koml\'os property (which can be considered an abstract version of the weak law of large numbers). The results rely on two previous papers from which we infer the fact that, like in the classical case of $L^1$, a subspace of a JBW$^*$-triple predual contains $\ell_1$ as soon as it contains uniform copies of $\ell_1^n$. Archive classification: math.OA math.FA Submitted from: aperalta(a)ugr.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1505.05302 or http://arXiv.org/abs/1505.05302

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Abstract of a paper by Christina Brech and Piotr Koszmider
by alspach＠math.okstate.edu 11 Jun '15

11 Jun '15

This is an announcement for the paper "An isometrically universal Banach space induced by a non-universal Boolean algebra" by Christina Brech and Piotr Koszmider. Abstract: Given a Boolean algebra $A$, we construct another Boolean algebra $B$ with no uncountable well-ordered chains such that the Banach space of real valued continuous functions $C(K_A)$ embeds isometrically into $C(K_B)$, where $K_A$ and $K_B$ are the Stone spaces of $A$ and $B$ respectively. As a consequence we obtain the following: If there exists an isometrically universal Banach space for the class of Banach spaces of a given uncountable density $\kappa$, then there is another such space which is induced by a Boolean algebra which is not universal for Boolean algebras of cardinality $\kappa$. Such a phenomenon cannot happen on the level of separable Banach spaces and countable Boolean algebras. This is related to the open question if the existence of an isometrically universal Banach space and of a universal Boolean algebra are equivalent on the nonseparable level (both are true on the separable level). Archive classification: math.FA math.GN math.LO Submitted from: piotr.math(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1505.04776 or http://arXiv.org/abs/1505.04776

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