Currently displaying 1 – 2 of 2

Showing per page

Order by Relevance | Title | Year of publication

Tight Embeddability of Proper and Stable Metric Spaces

F. Baudier;  G. Lancien — 2015

Analysis and Geometry in Metric Spaces

We introduce the notions of almost Lipschitz embeddability and nearly isometric embeddability. We prove that for p ∈ [1,∞], every proper subset of Lp is almost Lipschitzly embeddable into a Banach space X if and only if X contains uniformly the ℓpn’s. We also sharpen a result of N. Kalton by showing that every stable metric space is nearly isometrically embeddable in the class of reflexive Banach spaces.

A new metric invariant for Banach spaces

F. Baudier;  N. J. Kalton;  G. Lancien — 2010

Studia Mathematica

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.

Page 1

Download Results (CSV)