This is an announcement for the paper "Distortion in the finite determination result for embeddings of finite metric spaces into Banach spaces" by Sofiya Ostrovska and Mikhail I. Ostrovskii.
Abstract: Given a Banach space $X$ and a locally finite metric space $A$, it is known that if all finite subsets of $A$ admit bilipschitz embeddings into $X$ with distortions $\le C$, then the space $A$ itself admits an embedding into $X$ with distortion $\le D\cdot C$, where $D$ is an absolute constant. The goal of this paper is to show that $D>1$, implying that, in general, there is a ``deterioration of distortion'' in the aforementioned situations.
Archive classification: math.FA math.MG
Mathematics Subject Classification: 46B85, 46B20
Submitted from: ostrovsm@stjohns.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1510.05974
or