Workshop in Analysis and Probability Seminar

Date: July 19, 2018

Time: 3:00PM - 3:50PM

Location: BLOC 220

Speaker: Mikhail Ostrovskii, St. John's University

Title: Lipschitz free spaces on finite metric spaces

Abstract: Abstract: The main results of the talk: (1) For any finite metric space $M$ the Lipschitz free space on $M$ contains a large well-complemented subspace which is close to $\ell_1^n$. (2) Lipschitz free spaces on large classes of recursively defined sequences of graphs are not uniformly isomorphic to $\ell_1^n$ of the corresponding dimensions. These classes contain well-known families of diamond graphs and Laakso graphs. Interesting features of our approach are: (a) We consider averages over groups of cycle-preserving bijections of graphs which are not necessarily graph automorphisms; (b) In the case of such recursive families of graphs as Laakso graphs we use the well-known approach of Gr\"unbaum (1960) and Rudin (1962) for estimating projection constants in the case where invariant projections are not unique. Joint work with Stephen Dilworth and Denka Kutzarova