Different forms of metric characterizations of classes of Banach spaces
Mikhail I. Ostrovskii

TL;DR
This paper establishes an equivalence between embedding properties of Banach spaces and graph structures, providing a new metric characterization of classes of Banach spaces through finite graphs.
Contribution
It introduces a novel method linking Banach space embeddings with finite connected graphs, offering a new metric characterization framework.
Findings
Existence of finite connected graphs representing Banach space embeddings
Equivalence between uniform isomorphic and bilipschitz embeddings
Provides a new perspective on classifying Banach spaces
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.
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Taxonomy
TopicsAdvanced Banach Space Theory
