Different forms of metric characterizations of classes of Banach spaces

Details Different forms of metric characterizations of classes of Banach spaces Different forms of metric characterizations of classes of Banach spaces

2011-12-04

arxiv.org/abs/1112.0801v1

Mathematics

Functional Analysis

Accepted for publication in Houston Journal of Mathematics

Scientific paper

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.

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