arXiv subjects

F. Baudier

Publications and source records attributed to F. Baudier.

3 recordsLinked to original sources

arXiv2023

On stability of metric spaces and Kalton's property $Q$

The first named author introduced the notion of upper stability for metric spaces as a relaxation of stability. The motivation was a search for a new invariant to distinguish the class of reflexive Banach spaces from stable metric spaces in the coarse and uniform category. In this paper we show that property $Q$ does in fact imply upper stability. We also provide a direct proof of the fact that reflexive spaces are upper stable by relating the latter notion to the asymptotic structure of Banach spaces.

math.FA↗

arXiv2014

The metric geometry of the Hamming cube and applications

The Lipschitz geometry of segments of the infinite Hamming cube is studied. Tight estimates on the distortion necessary to embed the segments into spaces of continuous functions on countable compact metric spaces are given. As an application, the first nontrivial lower bounds on the $C(K)$-distortion of important classes of separable Banach spaces, where $K$ is a countable compact space in the family $ \{ [0,ω],[0,ω\cdot 2],\dots, [0,ω^2], \dots, [0,ω^k\cdot n],\dots,[0,ω^ω]\}\ ,$ are obtained.

math.FA↗

arXiv2009

A new metric invariant for Banach spaces

We show that if the Szlenk index of a Banach space $X$ is larger than the first infinite ordinal $ω$ or if the Szlenk index of its dual is larger than $ω$, then the tree of all finite sequences of integers equipped with the hyperbolic distance metrically embeds into $X$. We show that the converse is true when $X$ is assumed to be reflexive. As an application, we exhibit new classes of Banach spaces that are stable under coarse-Lipschitz embeddings and therefore under uniform homeomorphisms.

math.FA↗