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

http://arXiv.org/abs/1510.05974