Banach

banach@mathdept.okstate.edu

2549 discussions

Banach spaces webinar on Friday July 17 by Alejandro Chávez-Domínguez
by Sari, Bunyamin 15 Jul '20

15 Jul '20

Dear all, The next Banach spaces webinar is on Friday July 17 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Alejandro Chávez-Domínguez (University of Oklahoma) Title: Completely coarse maps are real-linear Abstract. In this talk I will present joint work with Bruno M. Braga, continuing the study of the nonlinear geometry of operator spaces that was recently started by Braga and Sinclair. Operator spaces are Banach spaces with an extra “noncommutative” structure. Their theory sometimes resembles very closely the Banach space case, but other times is very different. Our main result is an instance of the latter: a completely coarse map between operator spaces (that is, a map such that the sequence of its amplifications is equi-coarse) has to be real-linear. Continuing the search for an “appropriate” framework for a theory of the nonlinear geometry of operator spaces, we introduce a weaker notion of embeddability between them and show that it is strong enough for some applications. For instance, we show that if an infinite dimensional operator space X embeds in this weaker sense into Pisier's operator Hilbert space OH, then X must be completely isomorphic to OH. * For more information about the past and future talks, and videos please visit the webinar website http://www.math.unt.edu/~bunyamin/banach Upcoming schedule July 24: Florent Baudier (TAMU) Thank you, and best regards, Bunyamin Sari

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Banach spaces webinar on Friday 7/10 by Niels Laustsen
by Sari, Bunyamin 06 Jul '20

06 Jul '20

Dear all, The next Banach spaces webinar is on Friday July 10 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Niels Laustsen (Lancaster University) Title: A C(K) space with few operators and few decompositions Abstract. I shall report on joint work with Piotr Koszmider (IMPAN) concerning the closed subspace of $\ell_\infty$ generated by $c_0$ and the characteristic functions of elements of an uncountable, almost disjoint family $A$ of infinite subsets of the natural numbers. This Banach space has the form $C_0(K_A)$ for a locally compact Hausdorff space $K_A$ that is known under many names, including $\Psi$-space and Isbell--Mr\'ow\-ka space. We construct an uncountable, almost disjoint family $A$ such that the algebra of all bounded linear operators on $C_0(K_A)$ is as small as possible in the precise sense that every bounded linear operator on $C_0(K_A)$ is the sum of a scalar multiple of the identity and an operator that factors through $c_0$ (which in this case is equivalent to having separable range). This implies that $C_0(K_A)$ has the fewest possible decompositions: whenever $C_0(K_A)$ is written as the direct sum of two infinite-dimensional Banach spaces $X$ and $Y$, either $X$ is isomorphic to $C_0(K_A)$ and $Y$ to $c_0$, or vice versa. These results improve previous work of Koszmider in which an extra set-theoretic hypothesis was required. * For more information about the past and future talks, and videos please visit the webinar website http://www.math.unt.edu/~bunyamin/banach Upcoming schedule July 10: Alejandro Chávez-Domínguez (University of Oklahoma) Thank you, and best regards, Bunyamin Sari

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Announcement of New Papers
by Bentuo Zheng (bzheng) 01 Jul '20

01 Jul '20

Dear Subscribers, Please check the following link for updated list of papers for June, 2020. https://bentuo.wixsite.com/banach/banach-space-bulletin-board Best regards, Bentuo Zheng

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Banach spaces webinar on Friday 7/3 by Gilles Lancien
by Sari, Bunyamin 30 Jun '20

30 Jun '20

Dear all, The next Banach spaces webinar is on Friday July 3 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Gilles Lancien (Laboratoire de Mathématiques de Besançon) Title: Kalton's interlacing graphs and embeddings into dual Banach spaces Abstract. A fundamental theorem of Aharoni (1974) states that every separable metric spaces bi-Lipschitz embeds into $c_0$. It is a major open question to know whether any Banach space containing a Lipschitz copy of $c_0$ must contain a subspace linearly isomorphic to $c_0$. In this talk, we will consider similar questions in relation with the weaker notion of coarse embeddings. In a paper published in 2007, a major step was taken by Nigel Kalton, who showed that a Banach space containing a coarse copy of $c_0$ cannot have all its iterated duals separable (in particular it cannot be reflexive). However, it is still unknown whether such a space can be a separable dual. In this talk, we will discuss some aspects of this question. Kalton's argument is based on the use of a special family of metric graphs that we call Kalton's interlacing graphs. We will give results about dual spaces containing equi-Lipschitz or equi-coarse copies of these graphs, in relation with the Szlenk index, and show their optimality. This is a joint work with B. de Mendonça Braga, C. Petitjean and A. Procházka. * For more information about the past and future talks, and videos please visit the webinar website http://www.math.unt.edu/~bunyamin/banach Upcoming schedule July 10: Niels Laustsen (Lancaster University) Thank you, and best regards, Bunyamin Sari

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Banach spaces webinar on Friday 6/26 by Bruno Braga
by Sari, Bunyamin 24 Jun '20

24 Jun '20

Dear all, The next Banach spaces webinar is on Friday June 26 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Bruno Braga (University of Virginia) Title: Bringing uniform Roe algebras to Banach space theory Abstract. Given a metric space $X$, the uniform Roe algebra of $X$, denoted by $C^*_u(X)$, is a $C^*$-algebra which encodes many of $X$'s large scale geometric properties. In this talk, I will give an introduction on those objects and give an overview of the current state of the literature on questions related to rigidity of uniform Roe algebras (i.e., on how much of the large scale geometry of a metric space is encoded in its uniform Roe algebra). The second half of the talk will focus on bringing these mathematical objects to the context of Banach space/lattice theory. * For more information about the past and future talks, and videos please visit the webinar website http://www.math.unt.edu/~bunyamin/banach Upcoming schedule July 3: Gilles Lancien (Besançon) Thank you, and best regards, Bunyamin Sari

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Banach spaces webinar on Friday 6/19 by Christian Rosendal
by Sari, Bunyamin 15 Jun '20

15 Jun '20

Dear all, The next Banach spaces webinar is on Friday June 19 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Christian Rosendal (University of Illinois and NSF) Title: Two applications of Arens-Eells spaces to geometric group theory and abstract harmonic analysis Abstract. Arens-Eells spaces (aka Lipschitz free spaces or transportation cost spaces) give rise to interesting examples of Banach spaces and provide analytic techniques within Banach space geometry, but are also of importance as a tool for analysing objects outside Banach space theory using functional analytical techniques. I will present two such uses. The first is to abstract harmonic analysis where Arens-Eells spaces can be used to provide a very simple conceptual proof of a recent characterisation of amenability of topological groups due to F. M. Schneider and A. Thom. The second application is to the geometric study of topological groups, namely, to establish the Gromov correspondence between coarse equivalence and topological couplings in the widest possible setting. Time permitting, we also discuss some application of the harmonic analytical tools to the non-linear geometry of Banach spaces. * For more information about the past and future talks, and videos please visit the webinar website http://www.math.unt.edu/~bunyamin/banach Upcoming schedule June 26: Bruno Braga (University of Virginia) Thank you, and best regards, Bunyamin Sari

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Banach spaces webinar on Friday 6/12 by Noé de Rancourt
by Sari, Bunyamin 10 Jun '20

10 Jun '20

Dear all, The next Banach spaces webinar is on Friday June 12 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Noé de Rancourt (Kurt Gödel Research Center) Title: Local Banach-space dichotomies Abstract. I will present some results of a recent joint preprint with Wilson Cuellar Carrera and Valentin Ferenczi.<https://arxiv.org/abs/2005.06458> These results are generalizations of Banach-space dichotomies due to Gowers and to Ferenczi–Rosendal; the original dichotomies aimed at building a classification of separable Banach spaces "up to subspaces". Our generalizations are "local versions" of the original dichotomies, that is, we ensure that the outcome space can be taken in a prescribed family of subspaces. One of the most interesting examples of such a family is the family of all non-Hilbertian Banach spaces; hence, our results are a first step towards a classification of non-Hilbertian, $\ell_2$-saturated Banach spaces, up to subspaces. If time permits, I will present some applications of our work to a conjecture by Ferenczi and Rosendal about the number of subspaces of a separable Banach space. * For more information about the past and future talks, and videos please visit the webinar website http://www.math.unt.edu/~bunyamin/banach Upcoming schedule June 19: Christian Rosendal, University of Illinois at Chicago and NSF Thank you, and best regards, Bunyamin Sari

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Banach spaces webinar on Friday 6/5 by Denny Leung (National University of Singapore)
by Sari, Bunyamin 02 Jun '20

02 Jun '20

Dear all, The next Banach spaces webinar is on Friday June 5 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Denny Leung, National University of Singapore Title: Local convexity in $L^0$. Abstract. Let $(\Omega,\Sigma,\bP)$ be a nonatomic probability space and let $L^0(\Omega,\Sigma,\bP)$ be the space of all measurable functions on $(\Omega,\Sigma,\bP)$. We present some results characterizing the convex sets in $L^0$ that are locally convex with respect to the topology of convergence in measure. The work is motivated by results of Kardaras & Zitkovic (PAMS 2013) and Kardaras (JFA 2014) and is relevant to mathematical economics/finance. The talk is based on joint work with Niushan Gao and Foivos Xanthos: * A local Hahn-Banach Theorem and its applications, Arch. Math., 112(2019), 521-529. https://arxiv.org/abs/1809.01795 * On local convexity in $L^0$ and switching probability measures. https://arxiv.org/abs/1902.00992 * For more information about the past and future talks, and videos please visit the webinar website http://www.math.unt.edu/~bunyamin/banach Upcoming schedule June 12: Noé de Rancourt, Kurt Gödel Research Center Thank you, and best regards, Bunyamin

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Announcement of New Papers
by Bentuo Zheng (bzheng) 01 Jun '20

01 Jun '20

Dear Subscribers, Please check the following link for updated list of papers in May, 2020. https://bentuo.wixsite.com/banach/banach-space-bulletin-board Best, Bentuo Zheng

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Banach spaces webinar on Friday 5/29 by Miguel Martin
by Sari, Bunyamin 26 May '20

26 May '20

Dear all, The next Banach spaces webinar is on Friday May 29 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Miguel Martin (University of Granada) Title: On Quasi norm attaining operators between Banach spaces Abstract: This talk deals with a very recently introduced weakened notion of norm attainment for bounded linear operators. An operator $T\colon X \longrightarrow Y$ between the Banach spaces $X$ and $Y$ is quasi norm attaining if there is a sequence $(x_n)$ of norm one elements in $X$ such that $(Tx_n)$ converges to some $u\in Y$ with $\|u\|=\|T\|$. Norm attaining operators in the usual sense (i.e. operators for which there is a point in the unit ball where the norm of its image equals the norm of the operator) and compact operators satisfy this definition. The main result is that strong Radon-Nikodým operators (such as weakly compact operators can be approximated by quasi norm attaining operators (even by a stronger version of the definition), a result which does not hold for norm attaining operators. This allows us to give characterizations of the Radon-Nikodým property in term of the denseness of quasi norm attaining operators for both domain spaces and range spaces, extending previous results by Bourgain and Huff. We will also present positive and negative results on the denseness of quasi norm attaining operators, characterize both finite dimensionality and reflexivity in terms of quasi norm attaining operators, discuss conditions to obtain that quasi norm attaining operators are actually norm attaining, study the relationship with the norm attainment of the adjoint operator. We will finish the talk discussing some remarks and open questions. The content of the talk is based on the recent preprint On Quasi norm attaining operators between Banach spaces by Geunsu Choi, Yun Sung Choi, Mingu Jung, and Miguel Martin. * Please note that the new website for mathseminars.org is https://researchseminars.org/, which now lists seminars also from other sciences. (If you imported talk schedules to your calendar from mathseminars, you will have to delete and redo it from the new site.) * For more information about the past and future talks, and videos please visit the webinar website http://www.math.unt.edu/~bunyamin/banach Upcoming schedule June 5: Denny Leung (National University of Singapore) Thank you, and best regards, Bunyamin Sari

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