Abstract of a paper by Sofiya Ostrovska and Mikhail I. Ostrovskii
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
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