Banach

banach@mathdept.okstate.edu

2549 discussions

Announcement of Conference
by Bentuo Zheng (bzheng) 18 Jan '22

18 Jan '22

Dear All, We are organizing a workshop on Banach spaces and Banach lattices in Madrid. Further information can be found in the following link: https://www.icmat.es/congresos/2022/BSBL/participants.php With best regards, Antonio Aviles.

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Acta Sci Math (Szeged)
by Bentuo Zheng (bzheng) 18 Dec '21

18 Dec '21

News about the journal Acta Sci Math (Szeged) Acta Sci Math (Szeged) was founded and established by Alfréd Haar and Frigyes Riesz in 1922, currently it is the 15th oldest and still active journal in mathematics worldwide. You may agree that, although it was always a broad-in-scope journal, once it was one of the leading periodicals in the fields of functional analysis and operator theory. During its history, such outstanding mathematicians published here as (just to name a few of them in alphabetic order) T Ando, G Birkhoff, C Carathéodory, L Carleson, H Cartan, A Connes, P Erdős, L Fejér, M Fréchet, M G Krein, L Lovász, J von Neumann, H Rademacher, J Schauder, I Segal, J-P Serre, W Sierpiński, M H Stone, N Wiener, A Zygmund. I would like to inform you that on the 100th anniversary of its foundation, the journal is substantially renewed. This means several changes, the most important among them is that the Editorial Board has been extended, besides the editors in Szeged, the following scholars have joined the board: Franck Barthe, Institut de Mathématiques de Toulouse, France Libor Barto, Charles University, Prague, Czech Republic Hari Bercovici, Indiana University, Bloomington, USA Kenneth R. Davidson, University of Waterloo, Canada Robert M. Guralnick, University of Southern California, Los Angeles, USA Fumio Hiai, Tohoku University, Sendai, Japan Apoorva Khare, Indian Institute of Science, Bangalore, India Antonio M. Peralta University of Granada, Spain Gilles Pisier, Texas A&M University, College Station, USA Peter Šemrl, University of Ljubljana, Slovenia Péter Varjú, University of Cambridge, UK I would like to take this opportunity and call your attention to the renewed Acta Sci Math (Szeged) and kindly ask you to consider the journal for the publication of your quality papers. Please visit https://www.springer.com/journal/44146 Many thanks for your valuable contributions in advance! Lajos Molnár Editor-in-Chief

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Banach spaces webinar on 12/10 (tomorrow) by Chris Gartland (TAMU)
by Sari, Bunyamin 09 Dec '21

09 Dec '21

Hello all, We have a Banach spaces webinar on Friday 12/10 9AM by Chris Gartland of Texas A&M. Please use the following zoom link (different than the usual webinar link). -------------------------------------- Join Zoom Meeting https://tamu.zoom.us/j/92668666936?pwd=R2duYmxsQ0REakpIbzRDKzB0K3hwdz09 Meeting ID: 926 6866 6936 Passcode: 519913 --------------------------- Speaker: Chris Gartland (TAMU) Title: Non-embeddability of Carnot groups into $L^1$. Abstract: Motivated by the Goemans-Linial conjecture on the Sparsest Cut problem, Lee-Naor conjectured in 2006 that the Heisenberg group does not biLipschitz embed into $L^1$, and this was proven true by Cheeger-Kleiner in the same year. The Heisenberg group is the simplest example of a nonabelian Carnot group, and Cheeger-Kleiner noted that their non-embeddability proof should hold for any Carnot group $G$ satisfying the following regularity property: For every subset $E \subset G$ with finite perimeter, ``generic" metric-tangent spaces of $E$ at points in $\partial E$ are vertical half-spaces. It was expected that this property should hold for every nonabelian Carnot group, but at present, the problem remains open. The most significant achievement towards a solution is due to Ambrosio-Kleiner-Le Donne who proved that ``generic" \emph{iterated} metric-tangent spaces are vertical-half spaces. In this talk, we'll describe how intermediate results of Ambrosio-Kleiner-Le Donne together with an adaptation of the methods of Cheeger-Kleiner may be used to deduce the non-biLipschitz embeddability of nonabelian Carnot groups in $L^1$. Based on joint work with Sylvester Eriksson-Bique, Enrico Le Donne, Lisa Naples, and Sebastiano Nicolussi-Golo.

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Banach spaces webinar on Nov 19 by Krzysztof Święcicki
by Sari, Bunyamin 18 Nov '21

18 Nov '21

The next Banach spaces webinar is on Friday November 19 9AM Central time. Please join us at https://unt.zoom.us/j/83807914306 Title: No dimension reduction for doubling spaces of $\ell_q$ for $q>2$. Abstract: We'll provide a new elementary proof for the impossibility of dimension reduction for doubling subsets of $\ell_q$ for $q>2$. This is done by constructing a family of diamond graph-like objects based on the construction by Bartal, Gottlieb, and Neiman. We'll compare our approach with previous results and discuss their advantages and disadvantages. One noteworthy consequence of our proof is that it can be naturally generalized to obtain embeddability obstructions into non-positively curved spaces or asymptotically uniformly convex Banach spaces. Based on the work with Florent Baudier and Andrew Swift. For more information about the past and future talks, and videos please visit the webinar website http://www.math.unt.edu/~bunyamin/banach Best regards, Bunyamin Sari

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Banach spaces webinar on Nov 12 by Florent Baudier (Texas A&M)
by Sari, Bunyamin 11 Nov '21

11 Nov '21

Hello, The next Banach spaces webinar is on Friday November 12 9AM Central time. Please join us at https://unt.zoom.us/j/83807914306 Title: Umbel convexity and the geometry of trees Speaker: Florent Baudier (Texas A&M) Abstract. Markov convexity is a powerful invariant, introduced by Lee, Naor and Peres more than 15 years ago, which is related to the geometry of (locally finite) trees and (quantitative) uniformly convex renormings. In a joint work with Chris Gartland we introduced new metric invariants capturing the geometry of countably branching trees. Our main invariant, called umbel convexity, was inspired by Markov convexity and shares many of its desirable features. Most notably, it provides lower bounds on the distortion/compression required when embedding countably branching trees, and it is stable under certain nonlinear quotients. I will explain the close relationship between umbel convexity and Rolewicz's property $\beta$ renormings. If time permits, I will discuss the notion of umbel cotype, a relaxation of umbel convexity, and its relevance to the geometry of Heisenberg groups. 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 November 5 by Abraham Rueda Zoca (Universidad de Murcia)
by Sari, Bunyamin 04 Nov '21

04 Nov '21

Hello, The next Banach spaces webinar is on Friday November 5 9AM Central time. Please join us at https://unt.zoom.us/j/83807914306 Title: $L$-orthogonal elements and spaces of operators Speaker: Abraham Rueda Zoca (Universidad de Murcia) Abstract. Given a Banach space $X$, we say that an element $u\in X^{**}$ is $L$-orthogonal if, for every $x\in X$, it follows that $$\Vert x+u\Vert=\Vert x\Vert+\Vert u\Vert.$$ In 1989, G. Godefroy proved that a Banach space $X$ admits an equivalent renorming with non-zero $L$-orthogonal elements if, and only if, $X$ contains an isomorphic copy of $\ell_1$. Moreover, G. Godefroy and N. J. Kalton proved (in 1989 too) that a separable space $X$ has non-zero $L$-orthogonal elements if, and only if, the following condition holds: \begin{center} For every finite-dimensional subspace $F$ of $X$ and every $\varepsilon>0$ there exists $x\in S_X$ so that $\Vert y+\lambda x\Vert\geq (1-\varepsilon)(\Vert y\Vert+\vert\lambda\vert)$ holds for every $y\in F$ and every $\lambda\in\mathbb R$. \end{center} In this talk we will examine the validity of this theorem for non-separable Banach spaces. For this, and for other results of the structure of the set of $L$-orthogonal elements, the Banach spaces of linear bounded operators between two Banach spaces will play a crucial role. The author was supported by Juan de la Cierva-Formaci\'on fellowship FJC2019-039973, by MTM2017-86182-P (Government of Spain, AEI/FEDER, EU), by MICINN (Spain) Grant PGC2018-093794-B-I00 (MCIU, AEI, FEDER, UE), by Fundaci\'on S\'eneca, ACyT Regi\'on de Murcia grant 20797/PI/18, by Junta de Andaluc\'ia Grant A-FQM-484-UGR18 and by Junta de Andaluc\'ia Grant FQM-0185. 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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Colloquium by Thomas Schlumprecht on Oct 21 at UIUC
by Sari, Bunyamin 19 Oct '21

19 Oct '21

Dear all, There is a Math Colloquium talk at University of Illinois Urbana-Champagne on Thursday October 21 by Thomas Schlumprecht. The info is below. Please make sure to use the zoom link below and also note that it is on a different date and time than our usual webinars. Best, Bunyamin Join Zoom Meeting https://illinois.zoom.us/j/86232022920?pwd=SVg2UGhTSkN6TkxTdFhYZ1psNzAzQT09<https://nam04.safelinks.protection.outlook.com/?url=https%3A%2F%2Fillinois.…> Meeting ID: 862 3202 2920 Password: 999491 Speaker: Thomas Schlumprecht (Texas A&M) Title: Lamplighter metric spaces and their embeddings into $L_1$ Abstract: Understanding how a group or a graph, viewed as a geometric object, can be faithfully embedded into certain Banach spaces is a fundamental topic with applications to geometric group theory and theoretical computer science. In this joint work with Florent Baudier, Pavlos Motakis and Andras Zsak we observe that embeddings into random metrics can be fruitfully used to study the $L_1$-embeddability of lamplighter graphs or groups, and more generally lamplighter metric spaces. Once this connection has been established, several new upper bound estimates on the $L_1$-distortion of lamplighter metrics follow from known related estimates about stochastic embeddings into dominating tree-metrics. For instance, every lamplighter metric on a $n$-point metric space embeds bi-Lipschitzly into $L_1$ with distortion $O(\log n)$. In particular, for every finite group $G$ the lamplighter group $H = \mathbb{Z}_2\wr G$ bi-Lipschitzly embeds into $L_1$ with distortion $O(\log\log|H|)$. In the case where the ground space in the lamplighter construction is a graph with some topological restrictions, better distortion estimates can be achieved. Finally, we discuss how a coarse embedding into $L_1$ of the lamplighter group over the $d$-dimensional infinite lattice $\mathbb Z^d$ can be constructed from bi-Lipschitz embeddings of the lamplighter graphs over finite $d$-dimensional grids, and we include a remark on Lipschitz free spaces over finite metric spaces.

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Banach spaces webinar on Oct 15 by Pavlos Motakis
by Sari, Bunyamin 13 Oct '21

13 Oct '21

Hello, The next Banach spaces webinar is on Friday October 15 9AM Central time. Please join us at https://unt.zoom.us/j/83807914306 Title: Separable spaces of continuous functions as Calkin algebras Speaker: Pavlos Motakis, York University Abstract. The Calkin algebra $\mathcal{C}al(X)$ of a Banach space $X$ is the quotient algebra of all bounded linear operators $\mathcal{L}(X)$ on $X$ over the ideal of all compact ones $\mathcal{K}(X)$. A question that has gathered attention in recent years is what unital Banach algebras admit representations as Calkin algebras. There is a strong connection between quotients algebras of $\mathcal{L}(X)$ and the tight control of the operators on $X$ modulo a small ideal. We discuss a new contribution to this topic, namely that for every compact metric space $K$ there exists a Banach space $X$ so that $\mathcal{C}al(X)$ coincides isometrically with $C(K)$ as a Banach algebra. 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 (with the zoom link)
by Sari, Bunyamin 25 Aug '21

25 Aug '21

zoom link for the webinar which was missing in the first email: https://unt.zoom.us/j/83807914306 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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Annoucement
by Bentuo Zheng (bzheng) 25 Aug '21

25 Aug '21

Hi all, This is an open call for speakers for the webinar. If you wish to speak sometime in this academic year (September to May) please let me know so we can schedule it. Moreover, feel free to nominate speakers (e.g., grad students) who may not be on the email list. We had a very interesting two years of webinars with very impressive list of speakers and participants, and we wish to continue the tradition. Thank you all for your support. Best regards, Bunyamin

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