Seminar on Banach and Metric Space Geometry

Date: September 24, 2021

Time: 09:00AM - 10:00AM

Location: BLOC 302

Speaker: Audrey Fovelle, Université Bourgogne Franche-Comté

Title: Hamming graphs and concentration properties in Banach spaces

Abstract: In 2008, Kalton and Randrianarivony introduced a concentration property for Lipschitz maps defined on Hamming graphs, that every reflexive asymptotically uniformly smooth Banach space $X$ satisfies. This property, that we will note HFC_p,d, provides an obstruction to the coarse Lipschitz embedding of certain spaces into X. Later, Lancien, Raja and Causey proved that this result could be extended to quasi-reflexive spaces, by using a weaker concentration property, that we will call HIC_p,d. The goal of this talk is to show that these two properties are stable under l_p sums of Banach spaces, in order to obtain a non quasi-reflexive space that satisfies property HIC_p,d.