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