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Texas A&M University

Events for 08/04/2022 from all calendars

Workshop in Analysis and Probability Seminar

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Time: 3:00PM - 4:00PM

Location: BLOC 302

Speaker: Bunyamin Sari, University of North Texas

Title: On coarse (non)-universality of separable dual Banach spaces

Abstract: The talk is on obstructions to the coarse universality in separable dual Banach spaces. We will start with a basic idea of Kalton that many of the subsequent results are based on. We will recast those in a simpler framework. We prove an `asymptotic linearization' theorem for bounded maps from metric spaces $(\N^k, d)$ into Banach spaces with a boundedly complete basis. Then one can quickly deduce, for instance, the non-universality of reflexive spaces (Kalton), coarse rigidity of reflexive asymptotic-$c_0$ spaces (Baudier, Lancien, Motakis, and Schlumprecht), and non equi-coarse embedibility of Kalton graphs into the James space (Lancien, Petitjean, and Procházka). We will give two new results with some details of the proof. (1) Kalton's interlacing graphs do not equi-coarsely embed into the James tree space. (2) Banach spaces with a spreading basis are coarsely universal if and only if they contain a copy of $c_0$ linearly. Joint work with Steve Jackson (UNT) and Cory Krause (LeTourneau)