Banach

banach@mathdept.okstate.edu

2549 discussions

Banach spaces webinar on Friday 8/27 by Willian Corrêa, Universidade de São Paulo
by Sari, Bunyamin 25 Aug '21

25 Aug '21

Hello all, We are starting Banach spaces webinars for this academic year on Friday (8/27) with the following talk. Looking forward to seeing you all back. Best regards, Bunyamin For past talks and videos please see the webinar website: http://www.math.unt.edu/~bunyamin/banach ******** Speaker: Willian Corrêa (Universidade de São Paulo) Title: Two steps into the homology of $\ell_2$ Abstract. Enflo, Lindenstrauss and Pisier showed in 1975 the existence of a short exact sequence $0 \rightarrow \ell_2 \rightarrow X \rightarrow \ell_2 \rightarrow 0$ of Banach spaces and bounded linear operators in which $\ell_2$ is not complemented in $X$, i.e., $X \neq \ell_2$. This means that there is a non-Hilbertian Banach space with an isomorphic copy of $\ell_2$ such that the respective quotient is isomorphic to $\ell_2$ as well. In homological language, they showed that $Ext(\ell_2, \ell_2) \neq 0$. In this talk we discuss the next level of homology, i.e., we study exact sequences $0 \rightarrow \ell_2 \rightarrow X_1 \rightarrow X_2 \rightarrow \ell_2 \rightarrow 0$ and present the recent result that $Ext^2(\ell_2, \ell_2) \neq 0$. Joint work with Félix Cabello Sánchez, Jesús M. F. Castillo, Valentin Ferenczi and Ricardo García. The author was supported by FAPESP, processes 2016/25574-8 and 2018/03765-1.

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SUMIRFAS Schedule
by Bentuo Zheng (bzheng) 28 Jul '21

28 Jul '21

Dear all, The final schedule and abstracts for SUMIRFAS 2021 are available here. https://www.math.tamu.edu/~irinaholmes/SUMIRFAS21/SUMIRFAS2021.html The Zoom invitation is copied below. If you have not yet formally registered (even if your plan is to attend remotely), we would greatly appreciate for organizational purposes if you could please send a brief email to florent(a)tamu.edu<mailto:florent@tamu.edu> to notify us of your intent to attend the meeting. We look forward to seeing you, whether in-person or remotely, at SUMIRFAS 2021! Flo Baudier, on behalf of the organizers, Bill Johnson, Irina Holmes, Eviatar Procaccia.

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Annoucement of VOTCAM
by Bentuo Zheng (bzheng) 27 Jul '21

27 Jul '21

Hello, This is the 1st announcement for the 2021 Virginia Operator Theory and Complex Analysis Meeting (VOTCAM)<https://wordpress.us17.list-manage.com/track/click?u=ba58fb9fce1b5080748a2e…>, which will be held on Saturday, November, 13th at the University of Richmond and will be broadcast live on Zoom. Registration is free and open to all. Please pass this on to anyone who you think may be interested. If you are interested in attending in person or virtually please register at this link.<https://wordpress.us17.list-manage.com/track/click?u=ba58fb9fce1b5080748a2e…> Due to the uncertain future COVID restrictions, plans for an in-person VOTCAM may be changed. Please do not make any unalterable plans. VOTCAM features a mixture of speakers in Banach space theory, operator theory, operator algebras, and related areas. The speakers are listed below. The talks are each 30 or 50 minutes and will take place between 8:00am and 5:00pm EDT. VOTCAM 2021 speakers: Kevin Beanland – Washington & Lee University<https://wordpress.us17.list-manage.com/track/click?u=ba58fb9fce1b5080748a2e…> Michael Bush – University of Delaware<https://wordpress.us17.list-manage.com/track/click?u=ba58fb9fce1b5080748a2e…> Brian Lins – Hampden-Sydney College<https://wordpress.us17.list-manage.com/track/click?u=ba58fb9fce1b5080748a2e…> Diane Pelejo – College of William and Mary<https://wordpress.us17.list-manage.com/track/click?u=ba58fb9fce1b5080748a2e…> Thomas Schlumprecht – Texas A&M University<https://wordpress.us17.list-manage.com/track/click?u=ba58fb9fce1b5080748a2e…> Vrej Zarikian – United States Naval Academy<https://wordpress.us17.list-manage.com/track/click?u=ba58fb9fce1b5080748a2e…> VOTCAM is free and open to anyone and you can request to register at any time.<https://wordpress.us17.list-manage.com/track/click?u=ba58fb9fce1b5080748a2e…> Titles and abstracts of talks will be announced and posted soon. Again, please pass on this announcement to anyone that might be interested. The Organizing Committee: Kevin Beanland - Washington & Lee University Bill Ross - University of Richmond David Sherman - University of Virginia

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SUMIRFAS
by Bentuo Zheng (bzheng) 22 Jul '21

22 Jul '21

Dear Colleagues, We hope to find you all in good health. This Summer, SUMIRFAS 2021 will be the main event of the Workshop in Analysis and Probability at Texas A&M University. Due to ongoing travel restrictions, we will offer a hybrid version of the iconic SUMIRFAS event. This means that ALL talks will be available online but the talks will also be broadcasted LIVE in a lecture hall on campus! A few speakers will deliver their talks in person and on campus. Therefore, we will be happy to accommodate mathematicians who will be willing to attend the talks with other fellow participants on the Texas A&M campus while the SUMIRFAS will be happening. Dictated by the fluid sanitary situation, we might have to limit the number of participants on-campus in order to guarantee a safe and healthy environment. If you want to attend the talks remotely it is imperative that you register prior to SUMIRFAS 2021 so that we can send you the Zoom link before the SUMIRFAS begins. To formally register please contact Cara Starmer or one of the organizers: Bill Johnson, Irina Holmes, Eviatar Procaccia, or Flo Baudier. More practical information, contact information, the list of speakers, and the schedule are available here: https://www.math.tamu.edu/~irinaholmes/SUMIRFAS21/SUMIRFAS2021.html<https://urldefense.com/v3/__https:/www.math.tamu.edu/*irinaholmes/SUMIRFAS2…> We look forward to seeing you soon in Aggieland. Flo Baudier, on behalf of the organizers, Bill Johnson, Irina Holmes, Eviatar Procaccia.

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Banach spaces webinar on 7/16 by Rubén Medina (Granada)
by Sari, Bunyamin 15 Jul '21

15 Jul '21

Hello, The next Banach spaces webinar is on Friday July 16 at 9AM Central time. Please join us at https://unt.zoom.us/j/83807914306 Title: Compact retractions and the $\pi$-property of Banach spaces Speaker: Rubén Medina (Granada) Abstract: In the talk we will focus on Lipschitz retractions of a separable Banach space $X$ onto its closed and convex generating subsets $K$, a question asked by Godefroy and Ozawa in 2014. Our results are concerning the case when $K$ is in some quantitative sense small, namely when $K$ is in very little neibourhoods of certain finite dimensional sections of it. Under such assumptions we obtain a near characterization of the $\pi$-property (resp. Finite Dimensional Decomposition property) of a separable Banach space $X$. In one direction, if $X$ admits the Finite Dimensional Decomposition (which is isomorphically equivalent to the metric-$\pi$-property) then we will see how to construct a Lipschitz retraction onto a (small) generating convex compact $K$. On the other hand, we will prove that if $X$ admits a small (in a precise sense) generating compact Lipschitz retract then $X$ has the $\pi$-property. It seems to be an open problem whether the $\pi$-property is isomorphically equivalent to the metric-$\pi$-property (a positive answer would turn our results into a complete characterization). In the case of dual Banach spaces, this characterization is indeed valid. For more information about the past and future talks, and videos please visit the webinar website http://www.math.unt.edu/~bunyamin/banach Thank you, and best regards, Bunyamin Sari

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Banach spaces webinar on July 9 by Miguel Berasategui (University of Buenos Aires)
by Sari, Bunyamin 06 Jul '21

06 Jul '21

Hello, The next Banach spaces webinar is on Friday July 9 at 9AM Central time. Please join us at https://unt.zoom.us/j/83807914306 Title: Bidemocratic bases and their connections with other greedy-type bases Speaker. Miguel Berasategui (University of Buenos Aires) Abstract: In this talk we will focus on bidemocratic bases of Banach and quasi-Banach spaces, and their greedy-like properties. In particular, we will address the relation between bidemocratic bases and quasi-greedy bases. On the one hand, there are subspaces of $\ell_p$ with bidemocratic bases that are not quasi-greedy. On the other hand, for every arbitrary fundamental function $\varphi$, there is a Banach space with a bidemocratic, quasi-greedy conditional Schauder basis whose fundamental funcion grows as $\varphi$. For more information about the past and future talks, and videos please visit the webinar website http://www.math.unt.edu/~bunyamin/banach Thank you, and best regards, Bunyamin Sari

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Banach spaces webinar on July 2nd by Henrik Johannes Wirzenius (University of Helsinki)
by Sari, Bunyamin 01 Jul '21

01 Jul '21

Hello, The next Banach spaces webinar is on Friday July 2 at 9AM Central time. Please join us at https://unt.zoom.us/j/83807914306 Title: Closed ideals in the algebra of compact-by-approximable operators Speaker. Henrik Johannes Wirzenius (University of Helsinki) Abstract: In this talk I will present various examples of non-trivial closed ideals of the compact-by-approximable quotient algebra $\mathfrak A_X=\mathcal K(X)/\mathcal A(X)$ on Banach spaces $X$ failing the approximation property. Here $\mathcal K(X)$ denotes the algebra of compact operators $X\to X$ and $\mathcal A(X)=\overline{\mathcal F(X)}$ is the uniform norm closure of the bounded finite rank operators $\mathcal F(X)$. The examples include: (i) If $X$ has cotype 2, $Y$ has type 2, $\mathfrak A_X\neq\{0\}$ and $\mathfrak A_Y\neq\{0\}$, then $\mathfrak A_{X\oplus Y}$ has at least 2 (and in some cases up to 8) closed ideals. (ii) For all $4\lt p\lt \infty$ there are closed subspaces $X\subset\ell^p$ and $X\subset c_0$ such that $\mathfrak A_X$ has a non-trivial closed ideal. (iii) A Banach space $Z$ such that $\mathfrak A_Z$ contains an uncountable lattice of closed ideals. The talk is based on a recent preprint [arXiv:2105.08403] together with Hans-Olav Tylli (University of Helsinki). For more information about the past and future talks, and videos please visit the webinar website http://www.math.unt.edu/~bunyamin/banach Thank you, and best regards, Bunyamin Sari

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Announcement of A Talk
by Bentuo Zheng (bzheng) 24 Jun '21

24 Jun '21

Hello, The next Banach spaces webinar is on Friday June 18 at 9AM Central time. Please join us at https://unt.zoom.us/j/83807914306 Title: On the embeddability of the family of countably Branching trees into quasi-reflexive Banach spaces Speaker: Yoël Perreau (Besançon) Abstract. This talk will be centered on an asymptotic analogue of Bourgain's metric characterization of superreflexivity due to F. Baudier, N. Kalton and G. Lancien which can be reformulated as follows: the family $(T_N)$ of hyperbolic countably branching trees is a test family for the property $(\beta)$ of Rolewickz (also known as asymptotic superreflexivity) inside the class of reflexive Banach spaces. In other words a reflexive Banach space $X$ admits an equivalent norm with property $(\beta)$ if and only if it does not contain equi-Lipschitz the family $(T_N)$. We will explain how this result can be reformulated in terms of the values of the Szlenk index of the Banach space $X$ and of its dual space $X^*$ as written in the original paper and we will show how this characterization can be extended to the larger class of superreflexive Banach spaces. As a consequence we will answer the question of the embeddability of the family $(T_N)$ into the James space $\mathcal{J}$ and show that the non-embeddability of the family $(T_N)$ is not a sufficient condition for reflexivity. For more information about the past and future talks, and videos please visit the webinar website http://www.math.unt.edu/~bunyamin/banach

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Announcement of SUMIRFAS
by Bentuo Zheng (bzheng) 23 Jun '21

23 Jun '21

Dear Colleagues, We hope to find you all in good health. This Summer, SUMIRFAS 2021 will be the main event of the Workshop in Analysis and Probability at Texas A&M University. Due to ongoing travel restrictions, we will offer a hybrid version of the iconic SUMIRFAS event. This means that ALL talks will be available online but the talks will also be broadcasted LIVE in an amphitheater on campus! We expect that some speakers will be able to deliver their talks in person and on campus. Therefore, we will be happy to accommodate mathematicians who will be willing to attend the talks with other fellow participants on the Texas A&M campus while the SUMIRFAS will be happening. Dictated by the fluid sanitary situation, we might have to limit the number of participants on-campus in order to guarantee a safe and healthy environment. To register to SUMIRFAS 2021 (whether you will attend in person or remotely) please contact Cara Starmer or one of the organizers: Bill Johnson, Irina Holmes, Eviatar Procaccia, or Flo Baudier. More practical information, contact information, and the list of speakers is available here: https://www.math.tamu.edu/~irinaholmes/SUMIRFAS21/SUMIRFAS2021.html We look forward to seeing you in Aggieland soon. Flo Baudier, Bill Johnson, Irina Holmes, Eviatar Procaccia.

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Talk Annoucement
by Bentuo Zheng (bzheng) 17 Jun '21

17 Jun '21

Hello, Hope you all having a good summer break. The next Banach spaces webinar is on Friday June 18 at 9AM Central time. Please join us at https://unt.zoom.us/j/83807914306 Title: A discrete framework for interpolation of Banach spaces Speakers: Nick Lindemulder (Karlsruhe Institute of Technology) and Emiel Lorist (University of Helsinki) Abstract: We develop a discrete framework for the interpolation of Banach spaces, which contains e.g. the well-known real and complex interpolation methods, but also more exotic methods like the $\pm$-method, the Radamacher interpolation method and the $\ell^p$-interpolation method, as concrete examples. Our method is based on a sequential structure imposed on a Banach space and has both a formulation modelled after the real and the complex interpolation methods. For more information about the past and future talks, and videos please visit the webinar website http://www.math.unt.edu/~bunyamin/banach

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Banach