December 2015 - Banach - mathdept.okstate.edu

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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Informal Analysis Seminar at Kent State, November 14-15.
by Artem Zvavitch 14 Mar '16

14 Mar '16

Dear Colleague, The Analysis group at Kent State University is happy to announce a meeting of the Informal Analysis Seminar, which will be held at the Department of Mathematical Sciences at Kent State University, November 14-15, 2015. The plenary lecture series will be given by: Boaz Klartag (Tel Aviv University) and Igor Rivin (University of St. Andrews) Each speaker will deliver a four hour lecture series designed to be accessible for graduate students. Funding is available to cover the local and travel expenses of a limited number of participants. Graduate students, postdoctoral researchers, and members of underrepresented groups are particularly encouraged to apply for support. A poster session will be held for researchers to display their work. Graduate students are particularly encouraged to submit a poster. Posters can be submitted electronically in PDF format before November 6, 2015. Further information, and an online registration form, can be found online http://www.math.kent.edu/~zvavitch/informal/Informal_Analysis_Seminar/Novem… We encourage you to register as soon as possible, but to receive support and/or help with hotel reservation, please, register before October 1, 2015. Please feel free to contact us at informal(a)math.kent.edu for any further information. Sincerely, Analysis Group at Kent State University

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Abstract of a paper by Paul F.X. Muller and Johanna Penteker
by alspach＠math.okstate.edu 16 Dec '15

16 Dec '15

This is an announcement for the paper "Absolutely summing operators and atomic decomposition in bi-parameter Hardy spaces" by Paul F.X. Muller and Johanna Penteker. Abstract: For $f \in H^p(\delta^2)$, $0<p\leq 2$, with Haar expansion $f=\sum f_{I \times J}h_{I\times J}$ we constructively determine the Pietsch measure of the $2$-summing multiplication operator \[\mathcal{M}_f:\ell^{\infty} \rightarrow H^p(\delta^2), \quad (\varphi_{I\times J}) \mapsto \sum \varphi_{I\times J}f_{I \times J}h_{I \times J}. \] Our method yields a constructive proof of Pisier's decomposition of $f \in H^p(\delta^2)$ \[|f|=|x|^{1-\theta}|y|^{\theta}\quad\quad \text{ and }\quad\quad \|x\|_{X_0}^{1-\theta}\|y\|^{\theta}_{H^2(\delta^2)}\leq C\|f\|_{H^p(\delta^2)}, \] where $X_0$ is Pisier's extrapolation lattice associated to $H^p(\delta^2)$ and $H^2(\delta^2)$. Our construction of the Pietsch measure for the multiplication operator $\mathcal{M}_f$ involves the Haar coefficients of $f$ and its atomic decomposition. We treated the one-parameter $H^p$-spaces in [P.F.X M\"uller, J.Penteker, $p$-summing multiplication operators, dyadic Hardy spaces and atomic decomposition, Houston Journal Math.,41(2):639-668,2015.]. Archive classification: math.FA Mathematics Subject Classification: 42B30 46B25 46B09 46B42 46E40 47B10 60G42 Remarks: 10 pages Submitted from: johanna.penteker(a)jku.at The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1512.04790 or http://arXiv.org/abs/1512.04790

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Abstract of a paper by Geraldo Botelho, Jamilson R. Campos, and Joedson Santos
by alspach＠math.okstate.edu 16 Dec '15

16 Dec '15

This is an announcement for the paper "Operator ideals related to absolutely summing and Cohen strongly operators" by Geraldo Botelho, Jamilson R. Campos, and Joedson Santos. Abstract: We study the ideals of linear operators between Banach spaces determined by the transformation of vector-valued sequences involving the new sequence space introduced by Karn and Sinha \cite{karnsinha} and the classical spaces of absolutely, weakly and Cohen strongly summable sequences. As applications, we prove a new factorization theorem for absolutely summing operators and a contribution to the existence of infinite dimensional spaces formed by non-absolutely summing operators is given. Archive classification: math.FA Mathematics Subject Classification: 46B45, 47B10, 47L20 Remarks: 15 pages Submitted from: jamilson(a)dce.ufpb.br The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1512.04713 or http://arXiv.org/abs/1512.04713

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Abstract of a paper by Aicke Hinrichs, Anton Kolleck, and Jan Vybiral
by alspach＠math.okstate.edu 16 Dec '15

16 Dec '15

This is an announcement for the paper "Carl's inequality for quasi-Banach spaces" by Aicke Hinrichs, Anton Kolleck, and Jan Vybiral. Abstract: We prove that for any two quasi-Banach spaces $X$ and $Y$ and any $\alpha>0$ there exists a constant $c_\alpha>0$ such that $$ \sup_{1\le k\le n}k^{\alpha}e_k(T)\le c_\alpha \sup_{1\le k\le n} k^\alpha c_k(T) $$ holds for all linear and bounded operators $T:X\to Y$. Here $e_k(T)$ is the $k$-th entropy number of $T$ and $c_k(T)$ is the $k$-th Gelfand number of $T$. For Banach spaces $X$ and $Y$ this inequality is widely used and well-known as Carl's inequality. For general quasi-Banach spaces it is a new result, which closes a gap in the argument of Donoho in his seminal paper on compressed sensing. Archive classification: math.FA Remarks: 12 pages Submitted from: aicke.hinrichs(a)jku.at The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1512.04421 or http://arXiv.org/abs/1512.04421

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Abstract of a paper by Julio Becerra Guerrero, Gines Lopez-Perez, and Abraham Rueda
by alspach＠math.okstate.edu 16 Dec '15

16 Dec '15

This is an announcement for the paper "Octahedrality in Lipschitz free Banach spaces" by Julio Becerra Guerrero, Gines Lopez-Perez, and Abraham Rueda. Abstract: The aim of this note is to study octahedrality in vector valued Lipschitz-free Banach spaces on a metric space under topological hypotheses on it. As a consequence, we get that the space of Lipschitz functions on a metric space valued in a dual Banach space satisfies the weak-star strong diameter two property, under natural topological hipothesess on the metric space. Also, we show an example proving that these hypotheses are optimal. Archive classification: math.FA Remarks: 18 pages Submitted from: glopezp(a)ugr.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1512.03558 or http://arXiv.org/abs/1512.03558

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Abstract of a paper by Sergey V. Astashkin, Karol Lesnik, and Lech Maligranda
by alspach＠math.okstate.edu 16 Dec '15

16 Dec '15

This is an announcement for the paper "Isomorphic structure of Ces\`aro and Tandori spaces" by Sergey V. Astashkin, Karol Lesnik, and Lech Maligranda. Abstract: We investigate the isomorphic structure of the Ces\`aro spaces and their duals, the Tandori spaces. The main result states that the Ces\`aro function space $Ces_{\infty}$ and its sequence counterpart $ces_{\infty}$ are isomorphic, which answers to the question posted in \cite{AM09}. This is rather surprising since $Ces_{\infty}$ has no natural lattice predual similarly as the known Talagrand's example \cite{Ta81}. We prove that neither $ces_{\infty}$ is isomorphic to $l_{\infty}$ nor $Ces_{\infty}$ is isomorphic to the Tandori space $\widetilde{L_1}$ with the norm $\|f\|_{\widetilde{L_1}} =\|\widetilde{f}\|_{L_1},$ where $\widetilde{f}(t): \esssup_{s \geq t} |f(s)|.$ Our investigation involves also an examination of the Schur and Dunford-Pettis properties of Ces\`aro and Tandori spaces. In particular, using Bourgain's results we show that a wide class of Ces{\`a}ro-Marcinkiewicz and Ces{\`a}ro-Lorentz spaces have the latter property. Archive classification: math.FA Mathematics Subject Classification: 46E30, 46B20, 46B42 Submitted from: lech.maligranda(a)ltu.se The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1512.03336 or http://arXiv.org/abs/1512.03336

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Abstract of a paper by Bruno de Mendonca Braga
by alspach＠math.okstate.edu 16 Dec '15

16 Dec '15

This is an announcement for the paper "Coarse and uniform embeddings" by Bruno de Mendonca Braga. Abstract: In these notes, we study the relation between uniform and coarse embed= dings between Banach spaces. In order to understand this relation better, we al= so look at the problem of when a coarse embedding can be assumed to be topological. Among other results, we show that if a Banach space $X$ uniformly embeds into a minimal Banach space $Y$, then $X$ simultaneously coarsely and uniformly embeds into $Y$, and if a Banach space $X$ coarsely embeds into a minimal Banach space $Y$, then $X$ simultaneously coarsely and homeomorphically embeds into $Y$ by a map with uniformly continuous inverse. Archive classification: math.FA Mathematics Subject Classification: 46B80 Submitted from: demendoncabraga(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1512.03109 or http://arXiv.org/abs/1512.03109

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Abstract of a paper by Guillermo P. Curbera and Werner J. Ricker
by alspach＠math.okstate.edu 16 Dec '15

16 Dec '15

This is an announcement for the paper "Abstract Ces\`aro spaces: Integral representations" by Guillermo P. Curbera and Werner J. Ricker. Abstract: The Ces\`aro function spaces $Ces_p=[C,L^p]$, $1\le p\le\infty$, have received renewed attention in recent years. Many properties of $[C,L^p]$ are known. Less is known about $[C,X]$ when the Ces\`aro operator takes its values in a rearrangement invariant (r.i.) space $X$ other than $L^p$. In this paper we study the spaces $[C,X]$ via the methods of vector measures and vector integration. These techniques allow us to identify the absolutely continuous part of $[C,X]$ and the Fatou completion of $[C,X]$; to show that $[C,X]$ is never reflexive and never r.i.; to identify when $[C,X]$ is weakly sequentially complete, when it is isomorphic to an AL-space, and when it has the Dunford-Pettis property. The same techniques are used to analyze the operator $C:[C,X]\to X$; it is never compact but, it can be completely continuous. Archive classification: math.FA Mathematics Subject Classification: 46E30, 46G10 Remarks: 21 pages Submitted from: curbera(a)us.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1512.02760 or http://arXiv.org/abs/1512.02760

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Abstract of a paper by Mathieu Meyer and Shlomo Reisner
by alspach＠math.okstate.edu 16 Dec '15

16 Dec '15

This is an announcement for the paper "The isotropy constant and boundary properties of convex bodies" by Mathieu Meyer and Shlomo Reisner. Abstract: Let ${\cal K}^n$ be the set of all convex bodies in $\mathbb R^n$ endo= wed with the Hausdorff distance. We prove that if $K\in {\cal K}^n$ has posit= ive generalized Gauss curvature at some point of its boundary, then $K$ is no= t a local maximizer for the isotropy constant $L_K$. Archive classification: math.MG math.FA Mathematics Subject Classification: 46B20, 52A20, 53A05 Submitted from: reisner(a)math.haifa.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1512.02927 or http://arXiv.org/abs/1512.02927

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