Rigidity of AMN vector spaces

Details Rigidity of AMN vector spaces Rigidity of AMN vector spaces

2000-08-13

arxiv.org/abs/math/0008095v1

Mathematics

Functional Analysis

15 pages

Scientific paper

A metric vector space is asymptotically metrically normable (AMN) if there exists a norm asymptotically isometric to the distance. We prove that AMN vector spaces are rigid in the class of metric vector spaces under asymptotically isometric perturbations. This result follows from a general metric normability criterium. If the distance is translation invariant and satisfies an approximate multiplicative condition then there exists a lipschitz equivalent norm. Furthermore, we give necessary and sufficient conditions for the distance to be asymptotically isometric to the norm.

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