Banach

banach@mathdept.okstate.edu

2549 discussions

Abstract of a paper by Osamu Hatori
by Bentuo Zheng (bzheng) 01 Apr '18

01 Apr '18

This is an announcement for the paper “Isometries on Banach algebras of C(Y)-valued maps” by Osamu Hatori<https://arxiv.org/find/math/1/au:+Hatori_O/0/1/0/all/0/1>. Abstract: We propose a unified approach to the study of isometries on algebras of vector-valued Lipschitz maps and those of continuously differentiable maps by means of the notion of natural $C(Y)$-valuezations that take values in unital commutative $C^*$-algebras. A precise proof of a theorem of Jarosz \cite{ja} is exhibited. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1803.08236

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Abstract of a paper by Marek Balcerzak, Michał Popławski, Artur Wachowicz
by Bentuo Zheng (bzheng) 01 Apr '18

01 Apr '18

This is an announcement for the paper “Ideal convergent subseries in Banach spaces” by Marek Balcerzak<https://arxiv.org/find/math/1/au:+Balcerzak_M/0/1/0/all/0/1>, Michał Popławski<https://arxiv.org/find/math/1/au:+Poplawski_M/0/1/0/all/0/1>, Artur Wachowicz<https://arxiv.org/find/math/1/au:+Wachowicz_A/0/1/0/all/0/1>. Abstract: Assume that $\mathcal{I}$ is an ideal on $\mathbb{N}$, and $\sum_n x_n$ is a divergent series in a Banach space $X$. We study the Baire category, and the measure of the set $A(\mathcal{I}):=\{t\in\{0,1\}^{\mathbb{N}}: \sum_n t(n)x_n\textrm{is} \mathcal{I}-\textrm{convergent}\}$. In the category case, we assume that $\mathcal{I}$ has the Baire property and $\sum_n x_n$ is not unconditionally convergent, and we deduce that $A(\mathcal{I})$ is meager. We also study the smallness of $A(\mathcal{I})$ in the measure case when the Haar probability measure λ on {0,1}ℕ is considered. If $\mathcal{I}$ is analytic or coanalytic, and $\sum_n x_n$ is $\mathcal{I}$-divergent, then $\lambda(A(\mathcal{I}))=0$ which extends the theorem of Dindo\v{s}, \v{S}al\'at and Toma. Generalizing one of their examples, we show that, for every ideal $\mathcal{I}$ on $\mathbb{N}$, with the property of long intervals, there is a divergent series of reals such that $\lambda(A(Fin))=0$ and $\lambda(A(\mathcal{I}))=1$. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1803.03699

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Abstract of a paper by Stephen J. Dilworth, Denka Kutzarova, Vladimir Temlyakov, Ben Wallis
by Bentuo Zheng (bzheng) 01 Apr '18

01 Apr '18

This is an announcement for the paper “Weight-almost greedy bases” by Stephen J. Dilworth<https://arxiv.org/find/math/1/au:+Dilworth_S/0/1/0/all/0/1>, Denka Kutzarova<https://arxiv.org/find/math/1/au:+Kutzarova_D/0/1/0/all/0/1>, Vladimir Temlyakov<https://arxiv.org/find/math/1/au:+Temlyakov_V/0/1/0/all/0/1>, Ben Wallis<https://arxiv.org/find/math/1/au:+Wallis_B/0/1/0/all/0/1>. Abstract: We introduce the notion of a \textit{weight-almost greedy} basis and show that a basis for a real Banach space is w-almost greedy if and only if it is both quasi-greedy and w-democratic. We also introduce the notion of \textit{weight-semi-greedy} basis and show that a w-almost greedy basis is w-semi-greedy and that the converse holds if the Banach space has finite cotype. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1803.02932

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Abstract of a paper by Ioana Ghenciu
by Bentuo Zheng (bzheng) 01 Apr '18

01 Apr '18

This is an announcement for the paper “The p-Gelfand Phillips Property in Spaces of Operators and Dunford-Pettis like sets” by Ioana Ghenciu<https://arxiv.org/find/math/1/au:+Ghenciu_I/0/1/0/all/0/1>. Abstract: The $p$-Gelfand Phillips property $(1\leq p<\infty)$ is studied in spaces of operators. Dunford - Pettis type like sets are studied in Banach spaces. We discuss Banach spaces $X$ with the property that every $p$-convergent operator $T: X\rightarrow Y$ is weakly compact, for every Banach space $Y$. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1803.00351

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Abstract of a paper by Richard Lechner
by Bentuo Zheng (bzheng) 01 Apr '18

01 Apr '18

This is an announcement for the paper “Factorization in mixed norm Hardy and BMO spaces” by Richard Lechner<https://arxiv.org/find/math/1/au:+Lechner_R/0/1/0/all/0/1>. Abstract: Let $1\leq p, q<\infty$ and $1\leq r\leq\infty$. We show that the direct sum of mixed norm Hardy spaces $(\sum_n H_n^p(H_n^q))_r$ and the sum of their dual spaces $(\sum_n H_n^p(H_n^q)^*)_r$ are both primary. We do so by using Bourgain's localization method and solving the finite dimensional factorization problem. In particular, we obtain that the spaces $(\sum_n H_n^1(H_n^s))_r, (\sum_n H_n^1(H_n^s))_r)$, as well as $(\sum_n BMO_n(H_n^s))_r$ and $(\sum_n H_n^s(BMO_n))_r$, $1<s<\infty, 1\leq r\leq\infty$ are all primary.. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1610.01506

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Abstract of a paper by Richard Lechner
by Bentuo Zheng (bzheng) 01 Apr '18

01 Apr '18

This is an announcement for the paper “Dimension dependence of factorization problems: Hardy spaces and $SL_n^{\infty}$” by Richard Lechner<https://arxiv.org/find/math/1/au:+Lechner_R/0/1/0/all/0/1>. Abstract: Given $1\leq p<\infty$, let $W_n$ denote the finite-dimensional dyadic Hardy space $H_n^p$, its dual or $SL_n^{\infty}$”. We prove the following quantitative result: The identity operator on $W_n$ factors through any operator $T: W_N\rightarrow W_N$ which has large diagonal with respect to the Haar system, where $N$ depends \emph{linearly} on $n$. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1802.02857

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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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