July 2020 - Banach - mathdept.okstate.edu

Banach spaces webinar on Friday July 31 by Valentin Ferenczi
by Sari, Bunyamin 27 Jul '20

27 Jul '20

Dear all, The next Banach spaces webinar is on Friday July 31 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Valentin Ferenczi (University of São Paulo) Title: On envelopes and L_p-spaces Abstract. This talk is based on a work in progress with Jordi Lopez-Abad. We define, inside a given space $X$, the {\em envelope} ${\rm Env}(Y)$ of a subspace $Y$ as the largest subspace such that, for any net of surjective isometries on $X$, pointwise convergence to the identity on $Y$ implies pointwise convergence to the identity on ${\rm Env}(Y)$. This is reminiscent of the study of Korovkin sets in the spaces $C(0,1)$ or $L_p(\mu)$ (initiated by P.P. Korovkin in 1960). We shall mention some results of a recent paper of J. Lopez-Abad, B. Mbombo, and S. Todorcevic and myself (2019): different notions of ultrahomogeneity of Banach spaces will be stated (AUH, Fra\"iss\'e) which are relevant to multidimensional versions of Mazur rotations problem. Known examples of these are the Gurarij space and the spaces $L_p$'s for $p \neq 4,6,8,\ldots$. We shall address the conjecture that these are the only separable examples. The notion of envelope is especially relevant to the study of AUH or Fra\"iss\'e spaces. In particular we shall compute explicitely certain envelopes in $L_p$-spaces and conclude by giving a meaning to potentially new objects such as $L_p/\ell_2$, $L_p/L_q$, $L_p/\ell_q$, for appropriate values of $p$ and $q$. Partially supported by Fapesp, 2016/25574-8 and CNPq, 303731/2019-2. * 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 August 7: Pete Casazza (University of Missouri) Thank you, and best regards, Bunyamin Sari

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Banach spaces webinar on Friday July 24 by Florent Baudier
by Sari, Bunyamin 21 Jul '20

21 Jul '20

Dear all, The next Banach spaces webinar is on Friday July 24 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Florent Baudier (Texas A&M) Title: L_1-embeddability of lamplighter metrics Abstract. Lamplighter groups are important and well-studied objects in (geometric) group theory as they provide examples of groups with a variety of interesting geometric/algebraic properties. The lamplighter construction can naturally be extended to apply to graphs and is instrumental in the study of random walks on graphs. However, much remains to be understood regarding the embeddability of lamplighters groups or graphs into classical Banach spaces. Inspired by works on the earthmover distance I will explain how the machinery of stochastic embeddings into tree metrics can be fruitfully applied to the study of L_1-embeddability of lamplighter metrics and how it provides general upper bounds on the L_1-distortion of finite lamplighter graphs (and groups). I will then discuss an application to the coarse embeddability of the planar lamplighter group and if time permits an application to linear embeddings of Arens-Eells spaces over finite metric spaces into finite-dimensional l_1-spaces. The talk will be targeted towards non-specialists. Based on joint works with P. Motakis (UIUC), Th. Schlumprecht (Texas A&M), and A. Zsák (Peterhouse, Cambridge) * 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 31: Valentin Ferenczi (University of São Paulo) Thank you, and best regards, Bunyamin Sari

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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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