Spaces of small metric cotype
Metric Geometry
2010-09-20 v3 Functional Analysis
Abstract
Naor and Mendel's metric cotype extends the notion of the Rademacher cotype of a Banach space to all metric spaces. Every Banach space has metric cotype at least 2. We show that any metric space that is bi-Lipschitz equivalent to an ultrametric space has infinimal metric cotype 1. We discuss the invariance of metric cotype inequalities under snowflaking mappings and Gromov-Hausdorff limits, and use these facts to establish a partial converse of the main result.
Keywords
Cite
@article{arxiv.1001.3326,
title = {Spaces of small metric cotype},
author = {Ellen Veomett and Kevin Wildrick},
journal= {arXiv preprint arXiv:1001.3326},
year = {2010}
}
Comments
14 pages, the needed isometric inequality now derived from the literature, rather than proved by hand; other minor typos and errors fixed