This is an announcement for the paper "Different forms of metric characterizations of classes of Banach spaces" by Mikhail I. Ostrovskii.

Abstract: For each sequence X of finite-dimensional Banach spaces there exists a sequence H of finite connected nweighted graphs with maximum degree 3 such that the following conditions on a Banach space Y are equivalent: (1) Y admits uniformly isomorphic embeddings of elements of the sequence X. (2) Y admits uniformly bilipschitz embeddings of elements of the sequence H.

Archive classification: math.FA math.CO math.MG

Mathematics Subject Classification: Primary: 46B07, Secondary: 05C12, 46B85, 54E35

Remarks: Accepted for publication in Houston Journal of Mathematics

Submitted from: ostrovsm@stjohns.edu

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1112.0801

or

http://arXiv.org/abs/1112.0801