5 papers · 1 filter
Asymptotic and nonlinear geometries of Banach spaces and their interactions
Florent P. Baudier, Gilles Lancien
This book discusses the interactions between the (nonlinear) metric structure of Banach spaces and their linear asymptotic behavior. The overarching problem is to understand how th…
On asymptotic B-convexity and infratype
Florent Baudier, Audrey Fovelle
In this note, we introduce and study the notions of asymptotic B-convexity and asymptotic infratype , and we prove asymptotic analogs of a series of results due to Giesy \cite{G…
An asymptotic analog of a local-to-global phenomenon for uniformly convex renormings
Florent P. Baudier, Gilles Lancien
In this note, we investigate the renorming theory of Banach spaces with property of Rolewicz. In particular, we give a "coordinate-free" proof of the fact that every Banach s…
On stability of metric spaces and Kalton's property
F. Baudier, Th. Schlumprecht, A. Zsák
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 c…
The geometry of Hamming-type metrics and their embeddings into Banach spaces
Florent P. Baudier, Gilles Lancien, Pavlos Motakis +1
Within the class of reflexive Banach spaces, we prove a metric characterization of the class of asymptotic- spaces in terms of a bi-Lipschitz invariant which involves metrics…