Banach July 2016

banach@mathdept.okstate.edu

2 participants
12 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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for posting in the BBB
by GODEFROY Gilles 27 Jul '16

27 Jul '16

We are glad to announce the publication of the two volumes of the Kalton Selecta by Birkhauser, in the series ``Contemporary Mathematicians ». These two volumes (of about 780 pages each) gather 43 articles written by Nigel Kalton (1946-2010), sometimes with co-authors, with comments by experts of the many fields to which Nigel contributed, namely: F. Albiac, J. L. Ansorena, P. H. Enflo, D. H. Fremlin, A. Kaminska, B. Maurey, R. J. Elliott, F. Gesztesy, T. Kucherenko, G. Lancien, V. Peller, P. Portal, F. Sukochev, S. A. Ivanov, N. K. Nikolskii, I. E. Verbitsky, L. Weis, Y. A. Brudnyi, S. J. Dilworth, D. Kutzarova, Y. Benyamini, J. M. F. Castillo, H. G. Dales, M. I. Ostrovskii, G. Pisier, D. Werner, M. Cwikel, M. Milman, R. Rochberg, S. J.Dilworth, S. J. Montgomery-Smith. These Kalton Selecta are not only a tribute to an outstanding mathematician and his formidable contribution to functional analysis. They constitute a work in which every article is explained and put in its proper framework, in such a way that the reader gets easy access to advanced theories, through the efforts of the contributors. Their appearance is a scientific event for experts and beginners alike. Nigel Kalton’s work is a gold mine for anyone who is ready to read his lines - and in between. F. Gesztesy, G. Godefroy, L. Grafakos, I. Verbitsky.

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Abstract of a paper by Yisheng Song, Rudong Chen
by Bentuo Zheng (bzheng) 01 Jul '16

01 Jul '16

This is an announcement for the paper “Pazy's fixed point theorem with respect to the partial order in uniformly convex Banach spaces” by Yisheng Song<http://arxiv.org/find/math/1/au:+Song_Y/0/1/0/all/0/1>, Rudong Chen<http://arxiv.org/find/math/1/au:+Chen_R/0/1/0/all/0/1>. Abstract: In this paper, the Pazy's Fixed Point Theorems of monotone $\alpha$−nonexpansive mapping $T$ are proved in a uniformly convex Banach space $E$ with the partial order "$\leq$". That is, we obtain that the fixed point set of $T$ with respect to the partial order "$\leq$" is nonempty whenever the Picard iteration $\{T^n x_0\}$ is bounded for some initial point $x_0$ with $x_0\leq Tx_0$ or $Tx_0\leq x_0$. When restricting the demain of $T$ to the cone $P$, a monotone $\alpha$−nonexpansive mapping $T$ has at least a fixed point if and only if the Picard iteration $\{T^n0\}$ is bounbed. Furthermore, with the help of the properties of the normal cone $P$, the weakly and strongly convergent theorems of the Picard iteration $\{T^n x_0\}$ are showed for finding a fixed point of $T$ with respect to the partial order "$\leq$" in uniformly convex ordered Banach space. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1606.08216

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Abstract of a paper by Petr Hájek, Matěj Novotný
by Bentuo Zheng (bzheng) 01 Jul '16

01 Jul '16

This is an announcement for the paper “Some remarks on the structure of Lipschitz-free spaces” by Petr Hájek<http://arxiv.org/find/math/1/au:+Hajek_P/0/1/0/all/0/1>, Matěj Novotný<http://arxiv.org/find/math/1/au:+Novotny_M/0/1/0/all/0/1>. Abstract: We give several structural results concerning the Lipschitz-free spaces $F(M)$ where $M$ is a metric space. We show that $F(M)$ contains a complemented copy of $\ell_1(\Gamma)$, where $\Gamma=$dens$(M)$. If $\mathcal{N}$ is the net in a finite dimensional Banach space $X$, we show that $F(\mathcal{N})$ is isomorphic to its square. If $X$ contains a complemented copy of $\ell_p, c_0$ then $F(\mathcal{N})$ is isomorphic to its $\ell_1$-sum. Finally, we prove that for all $X\equiv C(K)$ spaces $F(\mathcal{N})$ are mutually isomorphic spaces with a Schauder basis. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1606.03926

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Abstract of a paper by C. Ward Henson, Yves Raynaud
by Bentuo Zheng (bzheng) 01 Jul '16

01 Jul '16

This is an announcement for the paper “Asymptotically Hilbertian Modular Banach Spaces: Examples of Uncountable Categoricity” by C. Ward Henson<http://arxiv.org/find/math/1/au:+Henson_C/0/1/0/all/0/1>, Yves Raynaud<http://arxiv.org/find/math/1/au:+Raynaud_Y/0/1/0/all/0/1>. Abstract: We give a criterion ensuring that the elementary class of a modular Banach space $E$ (that is, the class of Banach spaces, some ultrapower of which is linearly isometric to an ultrapower of $E$) consists of all direct sums $E\oplus_m H$, where $H$ is an arbitrary Hilbert space and $\oplus_m$ denotes the modular direct sum. Also, we give several families of examples in the class of Nakano direct sums of finite dimensional normed spaces that satisfy this criterion. This yields many new examples of uncountably categorical Banach spaces, in the model theory of Banach space structures. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1606.03122

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Abstract of a paper by Amra Rekic-Vukovic, Nermin Okicic, Ivan Arandjelovic
by Bentuo Zheng (bzheng) 01 Jul '16

01 Jul '16

This is an announcement for the paper “On modulus of noncompact convexity for a strictly minimalizable measure of noncompactness” by Amra Rekic-Vukovic<http://arxiv.org/find/math/1/au:+Rekic_Vukovic_A/0/1/0/all/0/1>, Nermin Okicic<http://arxiv.org/find/math/1/au:+Okicic_N/0/1/0/all/0/1>, Ivan Arandjelovic<http://arxiv.org/find/math/1/au:+Arandjelovic_I/0/1/0/all/0/1>. Abstract: In this paper we consider modulus of noncompact convexity $\Delta_{X, \Phi}$ associated with the strictly minimalizable measure of noncompactness $\Phi$. We also give some its properties and show its continuity on the interval $[0, \Phi(\bar{B}_X))$. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1606.01071

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Abstract of a paper by Amra Rekic-Vukovic, Nermin Okicic, Vedad Pasic, Ivan Arandjelovic
by Bentuo Zheng (bzheng) 01 Jul '16

01 Jul '16

This is an announcement for the paper “Continuity of modulus of noncompact convexity for minimalizable measures of noncompactness” by Amra Rekic-Vukovic<http://arxiv.org/find/math/1/au:+Rekic_Vukovic_A/0/1/0/all/0/1>, Nermin Okicic<http://arxiv.org/find/math/1/au:+Okicic_N/0/1/0/all/0/1>, Vedad Pasic<http://arxiv.org/find/math/1/au:+Pasic_V/0/1/0/all/0/1>, Ivan Arandjelovic<http://arxiv.org/find/math/1/au:+Arandjelovic_I/0/1/0/all/0/1>. Abstract: We consider the modulus of noncompact convexity $\Delta_{X, \Phi(\epsilon)}$ associated with the minimalizable measure of noncompactness $\Phi$. We present some properties of this modulus, while the main result of this paper is showing that $\Delta_{X, \Phi(\epsilon)}$ is a subhomogenous and continuous function on $[0, \Phi(\bar{B}_X))$ for an arbitrary minimalizable measure of compactness $\Phi$ in the case of a Banach space $X$ with the Radon-Nikodym property. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1606.01063

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Abstract of a paper by Anna Kamińska, Hyung-Joon Tag
by Bentuo Zheng (bzheng) 01 Jul '16

01 Jul '16

This is an announcement for the paper “Diameter of weak neighborhoods and the Radon-Nikodym property in Orlicz-Lorentz spaces” by Anna Kamińska<http://arxiv.org/find/math/1/au:+Kaminska_A/0/1/0/all/0/1>, Hyung-Joon Tag<http://arxiv.org/find/math/1/au:+Tag_H/0/1/0/all/0/1>. Abstract: Given an Orlicz convex function $\phi$ and a positive weight $w$ we present criteria of diameter two property and of Radon-Nikodym property in the Orlicz-Lorentz function and sequence spaces, $\Lambda_{\phi, w}$ and $\lambda_{\phi, w}$, respectively. We show that in the spaces $\Lambda_{\phi, w}$ or $\lambda_{\phi, w}$ equipped with the Luxemburg norm, the diameter of any relatively weakly subset of the unit ball in these spaces is two if and only if $\phi$ does not satisfy the appropriate growth condition $\Delta_2$, while they do have the Radon-Nikodym property if and only if $\phi$ satisfies the appropriate condition $\Delta_2$. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1606.00909

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Abstract of a paper by Malgorzata Czerwinska, Annna Kaminska
by Bentuo Zheng (bzheng) 01 Jul '16

01 Jul '16

This is an announcement for the paper “Banach Envelopes in Symmetric Spaces of Measurable Operators” by Malgorzata Czerwinska<http://arxiv.org/find/math/1/au:+Czerwinska_M/0/1/0/all/0/1>, Annna Kaminska<http://arxiv.org/find/math/1/au:+Kaminska_A/0/1/0/all/0/1>. Abstract: We study Banach envelopes for commutative symmetric sequence or function spaces, and noncommutative symmetric spaces of measurable operators. We characterize the class $(HC)$ of quasi-normed symmetric sequence or function spaces $E$ for which their Banach envelopes $\hat {E}$ are also symmetric spaces. The class of symmetric spaces satisfying $(HC)$ contains but is not limited to order continuous spaces. Let $\mathcal{M}$ be a non-atomic, semifinite von Neumann algebra with a faithful, normal, $\sigma$-finite trace $\tau$ and $E$ be as symmetric function space on $[0, \tau(1))$ or symmetric sequence space. We compute Banach envelope norms on $E(\mathcal{M}, \tau)$ and $C_E$ for any quasi-normed symmetric space $E$. Then we show under assumption that $E\in (HC)$ that the Banach envelope $\hat{E(\mathcal{M}, \tau)}$ of $E(\mathcal{M}, \tau)$ is equal to $\hat{E(\mathcal{M}, \tau)}$ isometrically. We also prove the analogous result for unitary matrix spaces $C_E$. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1606.00319

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Abstract of a paper by Elói M. Galego, Manuel González, Javier Pello
by Bentuo Zheng (bzheng) 01 Jul '16

01 Jul '16

This is an announcement for the paper “On subprojectivity and superprojectivity of Banach spaces” by Elói M. Galego<http://arxiv.org/find/math/1/au:+Galego_E/0/1/0/all/0/1>, Manuel González<http://arxiv.org/find/math/1/au:+Gonzalez_M/0/1/0/all/0/1>, Javier Pello<http://arxiv.org/find/math/1/au:+Pello_J/0/1/0/all/0/1>. Abstract: We obtain some results for and further examples of subprojective and superprojective Banach spaces. We also give several conditions providing examples of non-reflexive superprojective spaces; one of these conditions is stable under $c_0$-sums and projective tensor products. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1606.00308

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Banach July 2016