March 2018 - Banach - mathdept.okstate.edu

Informal Analysis Seminar February 24-25, 2018
by Artem Zvavitch 05 Sep '19

05 Sep '19

Dear Colleagues, 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, February 24-25. The seminar will feature plenary speakers Robert Connelly (Cornell University), and Peter Sternberg (Indiana University) 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. Further information, and an online registration form, can be found online http://www.math.kent.edu/informal We encourage you to register as soon as possible, but to receive support and/or help with hotel reservation, please register before January 29, 2018. Finally, please feel free to forward this email to any colleagues or students who you think may be interested in attending. Best regards, The Kent State Analysis Group

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BWB 2018 - registration and abstract submission
by Christina Brech 26 Mar '18

26 Mar '18

3rd Announcement of BWB 2018 Second Brazilian Workshop in Geometry of Banach Spaces August 13-17, 2018 Praia das Toninhas, Ubatuba, Sao Paulo State, Brazil. (Satellite Conference of the ICM 2018) We would like to remind you that we are organizing the Second Brazilian Workshop in Geometry of Banach Spaces BWB 2018, as a satellite conference of the ICM 2018. *Registration and abstract submission are now open and the deadline is May 15.* https://www.ime.usp.br/~banach/bwb2018/ The BWB will take place at the Wembley Inn Hotel, on the coast of Sao Paulo State, in Praia das Toninhas, Ubatuba, in the week August 13-17, 2018. The scientific program will focus on the theory of geometry of Banach spaces, with emphasis on the following directions: large scale geometry of Banach spaces; nonlinear theory; homological theory and set theory. The program includes a tutorial by Christian Rosendal, which will be accessible to graduate students. Additional scientific, practical and financial information can be found on website https://www.ime.usp.br/~banach/bwb2018/. Plenary speakers: S. A. Argyros (Nat. Tech. U. Athens) G. Godefroy (Paris 6) S. Grivaux* (U. Picardie Jules Verne) R. Haydon* (U. Oxford) W. B. Johnson (Texas A&M) J. Lopez-Abad (U. Paris 7) A. Naor* (U. Princeton) D. Pellegrino (UFPB) G. Pisier* (Paris 6 & Texas A&M) B. Randrianantoanina (Miami U.) C. Rosendal (U. Illinois Chicago) N. Weaver (Washington U.) (* to be confirmed) Scientific committee J. M. F. Castillo (U. Extremadura) R. Deville (U. Bordeaux) V. Ferenczi (U. Sao Paulo) M. Gonzalez (U. Cantabria) V. Pestov (U. Ottawa & UFSC) G. Pisier (U. Paris 6 & Texas A&M) D. Preiss (U. Warwick) B. Randrianantoanina (Miami U.) We are looking forward to meeting you next year in Brazil, C. Brech, L. Candido, W. Cuellar, V. Ferenczi and P. Kaufmann

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Sad news
by Pradipta Bandyopadhyay 23 Mar '18

23 Mar '18

With a heavy heart, I would like to inform you that Professor Ashoke Kumar Roy https://mathscinet.ams.org/mathscinet/search/author.html?mrauthid=209301 (Retd. Professor, ISI and my PhD supervisor) passed away yesterday (22 March) evening at 5:40 pm. Thanks and regards, Pradipta Bandyopadhyay ________________________________________________________________ * A smile is a curve that can set a lot of things straight * ************************************************* Professor Pradipta Bandyopadhyay Stat-Math Division Indian Statistical Institute 203 B T Road Kolkata 700108 INDIA E-mail : pradipta(a)isical.ac.in, pradiptabandyo(a)yahoo.co.uk Homepage : http://www.isical.ac.in/~pradipta/ Tel : +91-33-2575-3422 (O) ************************************************

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Abstract of a paper by Mohammed Bachir (UP1), Adrien Fabre
by Bentuo Zheng (bzheng) 04 Mar '18

04 Mar '18

This is an announcement for the paper “GÂteaux-Differentiability of Convex Functions in Infinite Dimension” by Mohammed Bachir<https://arxiv.org/find/math/1/au:+Bachir_M/0/1/0/all/0/1> (UP1), Adrien Fabre<https://arxiv.org/find/math/1/au:+Fabre_A/0/1/0/all/0/1>. Abstract: It is well known that in $R^n$ , G{\^a}teaux (hence Fr{\'e}chet) differ-entiability of a convex continuous function at some point is equivalent to the existence of the partial derivatives at this point. We prove that this result extends naturally to certain infinite dimensional vector spaces, in particular to Banach spaces having a Schauder basis. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1802.07633

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Abstract of a paper by Armando W. Gutiérrez
by Bentuo Zheng (bzheng) 04 Mar '18

04 Mar '18

This is an announcement for the paper “On the metric compactification of infinite-dimensional Banach spaces” by Armando W. Gutiérrez<https://arxiv.org/find/math/1/au:+Gutierrez_A/0/1/0/all/0/1>. Abstract: The notion of metric compactification was introduced by Gromov and later rediscovered by Rieffel; and has been mainly studied on proper geodesic metric spaces. We present here a generalization of the metric compactification that can be applied to infinite-dimensional Banach spaces. Thereafter we give a complete description of the metric compactification of infinite-dimensional $\ell_p$ spaces for all $1\leq p<\infty$. We also give a full characterization of the metric compactification of infinite-dimensional Hilbert spaces. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1802.04710

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Abstract of a paper by J F Toland
by Bentuo Zheng (bzheng) 04 Mar '18

04 Mar '18

This is an announcement for the paper “Localizing Weak Convergence in $L_{\infty}$” by J F Toland<https://arxiv.org/find/math/1/au:+Toland_J/0/1/0/all/0/1>. Abstract: For a general measure space $(X, \sL, \l)$ the pointwise nature of weak convergence in $\Li$ is investigated using singular functionals analogous to $\d$-functions in the theory of continuous functions on topological spaces. The implications for pointwise behaviour in $X$ of weakly convergent sequences in $\Li$ are inferred and the composition mapping $u\mapsto F(u)$ is shown to be sequentially weakly continuous on $\Li$ when $F:\RR \to \RR$ is continuous. When $\sB$ is the Borel $\sigma$-algebra of a locally compact Hausdorff topological space $(X, \rho)$ and $f \in L_\infty(X, \sB, \l)^*$ is arbitrary, let $\nu$ be the finitely additive measure in the integral representation of $f$ on $L_\infty(X, \sB, \l)$, and let $\hat{\nu}$ be the Borel measure in the integral representation of $f$ restricted to $C_0(X, \rho)$. From a minimax formula for $\hat{\nu}$ in terms $\nu$ it emerges that when $(X, \rho)$ is not compact, $\hat{\nu}$ may be zero when $\nu$ is not, and the set of $\nu$ for which $\hat{\nu}$ has a singularity with respect to $\l$ can be characterised. Throughout, the relation between $\d$-functions and the analogous singular functionals on $\Li$ is explored and weak convergence in $L_\infty(X,\sB,\l)$ is localized about points of $(X_{\infty}, \rho_{\infty})$, the one-point compactification of $(X, \rho)$. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1802.01878

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Abstract of a paper by Anna Kamińska, Yves Raynaud
by Bentuo Zheng (bzheng) 04 Mar '18

04 Mar '18

This is an announcement for the paper “Abstract Lorentz spaces and Köthe duality” by Anna Kamińska<https://arxiv.org/find/math/1/au:+Kaminska_A/0/1/0/all/0/1>, Yves Raynaud<https://arxiv.org/find/math/1/au:+Raynaud_Y/0/1/0/all/0/1>. Abstract: Given a fully symmetric Banach function space $E$ and a decreasing positive weight $w$ on $I=(0, a), 0<a\leq\infty$, the generalized Lorentz space $\Lambda_{E, w}$ is defined as the symmetrization of the canonical copy $E_w$ of $E$ on the measure space associated with the weight. If $E$ is an Orlicz space then $\Lambda_{E, w}$ is an Orlicz-Lorentz space. An investigation of the K\"othe duality of these classes is developed that is parallel to preceding works on Orlicz-Lorentz spaces. First a class of functions $M_{E, w}$, which does not need to be even a linear space, is similarly defined as the symmetrization of the space $w.E_w$. Let also $Q_{E, w}$ be the smallest fully symmetric Banach function space containing $M_{E, w}$. Then the K\"othe dual of the class $M_{E, w}$ is identified as the Lorentz space $\Lambda_{E’, w}$, while the K\"othe dual of $\Lambda_{E, w}$ is Q_{E’, w}$. The space $Q_{E, w}$ is also characterized in terms of Halperin's level functions. These results are applied to concrete Banach function spaces. In particular the K\"othe duality of Orlicz-Lorentz spaces is revisited at the light of the new results. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1802.01728

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Abstract of a paper by Leandro Candido
by Bentuo Zheng (bzheng) 04 Mar '18

04 Mar '18

This is an announcement for the paper “On the geometry of the Banach spaces $C([0, \alpha]\times K)$ for some scattered ♣-compacta” by Leandro Candido<https://arxiv.org/find/math/1/au:+Candido_L/0/1/0/all/0/1>. Abstract: For some non-metrizable scattered $K$ compacta, constructed under the assumption of the Ostaszewski's ♣-principle, we study the geometry of the Banach spaces of the form $C(M\times K)$ where $M$ is a countable compact metric space. In particular, we classify up to isomorphism all the complemented subspaces of $C([0, \omega]\times K)$ and $C([0, \omega^{\omega}]\times K)$. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1802.01164

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