Banach

banach@mathdept.okstate.edu

2549 discussions

Abstract of a paper by Aude Dalet
by alspach＠math.okstate.edu 16 Apr '14

16 Apr '14

This is an announcement for the paper "Free spaces over some proper metric spaces" by Aude Dalet. Abstract: We prove that the Lipschitz-free space over a countable proper metric space and over a proper ultrametric space is isometric to a dual space and has the metric approximation property. Archive classification: math.FA Mathematics Subject Classification: 46B10, 46B28 Submitted from: aude.dalet(a)univ-fcomte.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1404.3939 or http://arXiv.org/abs/1404.3939

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Abstract of a paper by Jan van Neerven, Mark Veraar, and Lutz Weis
by alspach＠math.okstate.edu 16 Apr '14

16 Apr '14

This is an announcement for the paper "On the R-boundedness of stochastic convolution operators" by Jan van Neerven, Mark Veraar, and Lutz Weis. Abstract: The $R$-boundedness of certain families of vector-valued stochastic convolution operators with scalar-valued square integrable kernels is the key ingredient in the recent proof of stochastic maximal $L^p$-regularity, $2<p<\infty$, for certain classes of sectorial operators acting on spaces $X=L^q(\mu)$, $2\le q<\infty$. This paper presents a systematic study of $R$-boundedness of such families. Our main result generalises the afore-mentioned $R$-boundedness result to a larger class of Banach lattices $X$ and relates it to the $\ell^{1}$-boundedness of an associated class of deterministic convolution operators. We also establish an intimate relationship between the $\ell^{1}$-boundedness of these operators and the boundedness of the $X$-valued maximal function. This analysis leads, quite surprisingly, to an example showing that $R$-boundedness of stochastic convolution operators fails in certain UMD Banach lattices with type $2$. Archive classification: math.FA math.PR Mathematics Subject Classification: Primary: 60H15, Secondary: 42B25, 46B09, 46E30, 60H05 Submitted from: m.c.veraar(a)tudelft.nl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1404.3353 or http://arXiv.org/abs/1404.3353

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Abstract of a paper by Michael Cwikel, Mario Milman and Richard Rochberg
by alspach＠math.okstate.edu 16 Apr '14

16 Apr '14

This is an announcement for the paper "An introduction to Nigel Kalton's work on differentials of complex interpolation processes for Kothe spaces" by Michael Cwikel, Mario Milman and Richard Rochberg. Abstract: This paper contains no new results. It is intended to be merely a brief introduction to the long paper: N. J. Kalton, Differentials of complex interpolation processes for Kothe function spaces. Trans. Amer. Math. Soc. 333 (1992), no. 2, 479--529. and to mention some possible directions for applying the powerful methods developed in Kalton's paper for further future research. The reader should also be aware of other perspectives in other commentaries on Kalton's paper, which appear in other sources to which we refer. Archive classification: math.FA Mathematics Subject Classification: 46B70 (Primary), 42B20, 42B30, 42B35, 46B42 (Secondary) Remarks: 12 pages Submitted from: mcwikel(a)math.technion.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1404.2893 or http://arXiv.org/abs/1404.2893

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Abstract of a paper by O. Blasco, G. Botelho, D, Pellegrino, and P. Rueda
by alspach＠math.okstate.edu 16 Apr '14

16 Apr '14

This is an announcement for the paper "Absolutely summing multilinear operators on $\ell_p$ spaces" by O. Blasco, G. Botelho, D, Pellegrino, and P. Rueda. Abstract: We prove new summability properties for multilinear operators on $\ell_p$ spaces. An important tool for this task is a better understanding of the interplay between almost summing and absolutely summing multilinear operators. 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/1404.1322 or http://arXiv.org/abs/1404.1322

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Abstract of a paper by Arnaud Marsiglietti
by alspach＠math.okstate.edu 16 Apr '14

16 Apr '14

This is an announcement for the paper "On improvement of the concavity of convex measures" by Arnaud Marsiglietti. Abstract: We prove that a general class of measures, which includes $\log$-concave measures, are $\frac{1}{n}$-concave in the terminology of Borell under additional assumptions on the measure or on the sets, such as symmetries. This generalizes results of Gardner and Zvavitch. Archive classification: math.FA Submitted from: arnaud.marsiglietti(a)univ-mlv.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1403.7643 or http://arXiv.org/abs/1403.7643

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Abstract of a paper by Daniel Carando, Andreas Defant, and Pablo Sevilla-Peris
by alspach＠math.okstate.edu 16 Apr '14

16 Apr '14

This is an announcement for the paper "A note on a Bohnenblust-Hille-Helson type inequality" by Daniel Carando, Andreas Defant, and Pablo Sevilla-Peris. Abstract: We give a variant of the Bohenblust-Hille inequality which, for certain families of polynomials, leads to constants with polynomial growth in the degree. Archive classification: math.FA Submitted from: psevilla(a)mat.upv.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1403.7033 or http://arXiv.org/abs/1403.7033

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Abstract of a paper by Mehdi Ghasemi
by alspach＠math.okstate.edu 16 Apr '14

16 Apr '14

This is an announcement for the paper "Integral representation of linear functionals on function spaces" by Mehdi Ghasemi. Abstract: Let $A$ be a vector space of real valued functions on a non-empty set $X$ and $L:A\rightarrow\mathbb{R}$ a linear functional. Given a $\sigma$-algebra $\mathcal{A}$, of subsets of $X$, we present a necessary condition for $L$ to be representable as an integral with respect to a measure $\mu$ on $X$ such that elements of $\mathcal{A}$ are $\mu$-measurable. This general result then is applied to the case where $X$ carries a topological structure and $A$ is a family of continuous functions and naturally $\mathcal{A}$ is the Borel structure of $X$. As an application, short solutions for the full and truncated $K$-moment problem are presented. An analogue of Riesz-Markov-Kakutani representation theorem is given where $C_{c}(X)$ is replaced with whole $C(X)$. Then we consider the case where $A$ only consists of bounded functions and hence is equipped with $\sup$-norm. Archive classification: math.FA Mathematics Subject Classification: 47A57, 28C05, 28E99 Submitted from: mehdi.ghasemi(a)usask.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1403.6956 or http://arXiv.org/abs/1403.6956

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Abstract of a paper by Pedro Levit Kaufmann
by alspach＠math.okstate.edu 16 Apr '14

16 Apr '14

This is an announcement for the paper "Products of Lipschitz-free spaces and applications" by Pedro Levit Kaufmann. Abstract: We show that, given a Banach space $X$, the Lipschitz-free space over $X$, denoted by $\mathcal{F}(X)$, is isomorphic to $(\sum_{n=1}^\infty \mathcal{F}(X))_{\ell_1}$. Some applications are presented, including a non-linear version of Pe\l czy\'ski's decomposition method for Lipschitz-free spaces and the identification up to isomorphism between $\mathcal{F}(\mathbb{R}^n)$ and the Lipschitz-free space over any compact metric space which is locally bi-Lipschitz embeddable into $\mathbb{R}^n$ and which contains a subset that is Lipschitz equivalent to the unit ball of $\mathbb{R}^n$. We also show that $\mathcal{F}(M)$ is isomorphic to $\mathcal{F}(c_0)$ for all separable metric spaces $M$ which are absolute Lipschitz retracts and contain a subset which is Lipschitz equivalent to the unit ball of $c_0$. This class contains all $C(K)$ spaces with $K$ infinite compact metric (Dutrieux and Ferenczi had already proved that $\mathcal{F}(C(K))$ is isomorphic to $\mathcal{F}(c_0)$ for those $K$ using a different method). Finally we study Lipschitz-free spaces over certain unions and quotients of metric spaces, extending a result by Godard. Archive classification: math.FA Mathematics Subject Classification: Primary 46B20, Secondary 46T99 Remarks: 17 pages, 1 figure Submitted from: pkaufmann(a)math.jussieu.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1403.6605 or http://arXiv.org/abs/1403.6605

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Abstract of a paper by Cedric Arhancet
by alspach＠math.okstate.edu 16 Apr '14

16 Apr '14

This is an announcement for the paper "On a conjecture of Pisier on the analyticity of semigroups" by Cedric Arhancet. Abstract: We show that the analyticity of some semigroups $(T_t)_{t \geq 0}$ of contractive Fourier multipliers on $L^p$-spaces of compact abelian groups is preserved by the tensorisation of the identity operator of a Banach space for a large class of K-convex Banach spaces, answering partially a conjecture of Pisier. We also give versions of this result for some semigroups of Schur multipliers and Fourier multipliers on noncommutative $L^p$-spaces. Finally, we give a precise description of semigroups of Schur multipliers to which the result of this paper can be applied. Archive classification: math.FA Remarks: 10 pages; comments are welcome Submitted from: cedric.arhancet(a)univ-fcomte.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1403.6737 or http://arXiv.org/abs/1403.6737

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Abstract of a paper by Daniel Carando and Martin Mazzitelli
by alspach＠math.okstate.edu 16 Apr '14

16 Apr '14

This is an announcement for the paper "Bounded holomorphic functions attaining their norms in the bidual" by Daniel Carando and Martin Mazzitelli. Abstract: Under certain hypotheses on the Banach space $X$, we prove that the set of analytic functions in $\mathcal{A}_u(X)$ (the algebra of all holomorphic and uniformly continuous functions in the ball of $X$) whose Aron-Berner extensions attain their norms, is dense in $\mathcal{A}_u(X)$. The result holds also for functions with values in a dual space or in a Banach space with the so-called property $(\beta)$. For this, we establish first a Lindenstrauss type theorem for continuous polynomials. We also present some counterexamples for the Bishop-Phelps theorem in the analytic and polynomial cases where our results apply. Archive classification: math.FA Submitted from: mmazzite(a)dm.uba.ar The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1403.6431 or http://arXiv.org/abs/1403.6431

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