February 2016 - Banach - mathdept.okstate.edu

[Banach Space Bulletin Board] Abstract of a paper by Mona Nabiei
by Bentuo Zheng (bzheng) 28 Feb '16

28 Feb '16

This is an announcement for the paper “An effective metric on $C(H,K)$ with normal structure” by Mona Nabiei. Abstract: This study first defines a new metric with normal structure on $C(H,K)$ and then a new technique to prove fixed point theorems for families of non-expansive maps on this metric space. Indeed, it shows that the presence of a bounded orbit implies the existence of a fixed point for a group of h-biholomorphic automorphisms on $C(H,K)$. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1602.04015

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[Banach Space Bulletin Board] Abstract of a paper by Constantin Costara and Dusan Repov
by Bentuo Zheng (bzheng) 28 Feb '16

28 Feb '16

This is an announcement for the paper “Spectral isometries onto algebras having a separating family of finite-dimensional irreducible representations” by Constantin Costara and Dusan Repov. Abstract: We prove that if $\mathcal{A}$ is a complex, unital semisimple Banach algebra and $\mathcal{B}$ is a complex, unital Banach algebra having a separating family of finite-dimensional irreducible representations, then any unital linear operator from $\mathcal{A}$ onto $\mathcal{B}$ which preserves the spectral radius is a Jordan morphism. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1602.03964

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[Banach Space Bulletin Board] Abstract of a paper by M. Maia, D. Pellegrino and J. Santos
by Bentuo Zheng (bzheng) 28 Feb '16

28 Feb '16

This is an announcement for the paper “An index of summability for pairs of Banach spaces” by M. Maia, D. Pellegrino and J. Santos. Abstract: We introduce the notion of index of summability for pairs of Banach spaces; for Banach spaces E; F, this index plays the role of a kind of measure of how the m-homogeneous polynomials from E to F are far from being absolutely summing. In some cases the optimal index of summability is computed. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1602.03363

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[Banach Space Bulletin Board] Abstract of a paper by R. M. Lochowski
by Bentuo Zheng (bzheng) 28 Feb '16

28 Feb '16

This is an announcement for the paper “Riemann-Stieltjes integrals driven by irregular signals in Banach spaces and rate-independent characteristics of their irregularity” by R. M. Lochowski. Abstract: Using truncated variation techniques we derive a new theorem on the existence of the Riemann-Stieltjes integral driven by irregular signals in Banach spaces. Next, for any $p\geq 1$ we introduce the space of regulated functions $f: [a, b]\rightarrow W$ ($a<b$ are real numbers and $W$ is a Banach space), which may be uniformly approximated with accuracy $\delta>0$ by functions whose total variation is of order $\delta_{1-p}$ as $\delta\rightarrow 0+$. As an application of these results we derive more exact, rate-independent characterisations of the irregularity of the integrals driven by irregular signals. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1602.02269

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[Banach Space Bulletin Board] Abstract of a paper by R. Chill and Yu. Tomilov
by Bentuo Zheng (bzheng) 28 Feb '16

28 Feb '16

This is an announcement for the paper “Operators $L^1 (\mathbb R_+ )\to X$ and the norm continuity problem for semigroups” by R. Chill and Yu. Tomilov. Abstract: We present a new method for constructing $C_0$-semigroups for which properties of the resolvent of the generator and continuity properties of the semigroup in the operator-norm topology are controlled simultaneously. It allows us to show that a) there exists a $C_0$--semigroup which is continuous in the operator-norm topology for $t\in [0,1]$ such that the resolvent of its generator has a logarithmic decay at infinity along vertical lines; b) there exists a $C_0$--semigroup which is continuous in the operator-norm topology for no $t\in R_+$ such that the resolvent of its generator has a decay along vertical lines arbitrarily close to a logarithmic one. These examples rule out any possibility of characterizing norm-continuity of semigroups on arbitrary Banach spaces in terms of resolvent-norm decay on vertical lines. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1602.01163

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[Banach Space Bulletin Board] Abstract of a paper by D. Candeloro, L. Di Piazza, K. Musial and A. R. Sambuchini
by Bentuo Zheng (bzheng) 28 Feb '16

28 Feb '16

This is an announcement for the paper “Gauge integrals and selections of weakly compact valued multifunctions” by D. Candeloro, L. Di Piazza, K. Musial and A. R. Sambuchini. Abstract: In the paper Henstock, McShane, Birkhoff and variationally multivalued integrals are studied for multifunctions taking values in the hyperspace of convex and weakly compact subsets of a general Banach space X. In particular the existence of selections integrable in the same sense of the corresponding multifunctions has been considered. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1602.00473

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Texas A&M 2016 Concentration Week: Metric Spaces: Analysis, Embeddings into Banach Spaces, Applications
by Florent P. Baudier 14 Feb '16

14 Feb '16

Dear colleagues, Tuesday July 5- Saturday July 9, 2016 there will be a Concentration Week, "Metric Spaces: Analysis, Embeddings into Banach Spaces, Applications", organized by Florent Baudier, Mikhail Ostrovskii, Lova Randrianarivony and Thomas Schlumprecht. The Concentration Week aims to bring together researchers in analysis on metric spaces, discrete geometry, nonlinear Banach space geometry, and geometric group theory, and to facilitate further interaction among researchers in these fields. The homepage of the Concentration Week is located at http://www.math.tamu.edu/~florent/cw2016.html For information about the Concentration Week "Metric Spaces: Analysis, Embeddings into Banach Spaces, Applications", please contact Florent Baudier <florent at math.tamu.edu>. This concentration week is sponsored by the Workshop in Analysis and Probability at Texas A&M. You can get some information about the Workshop from the home page, URL http://www.math.tamu.edu/~kerr/workshop/ 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, please contact Cara Starmer <cara at math.tamu.edu>. For more information on the Workshop itself, please contact William Johnson <johnson at math.tamu.edu>, David Kerr <kerr at math.tamu.edu>, or Gilles Pisier <pisier at math.tamu.edu>. Sincerely, F. Baudier (Texas A&M University), for the organizing committee: M. Ostrovskii (St John's University), N. Randrianarivony (St Louis University), Th. Schlumprecht (Texas A&M University). -- Florent P. Baudier Visiting Assistant Professor Department of Mathematics Texas A&M University Office: Blocker 525C webpage : http://www.math.tamu.edu/~florent/ Mailstop 3368 | College Station, TX 77843 Fax. 979.845.6028

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