Sphere equivalence, Banach expanders, and extrapolation
Group Theory
2015-06-29 v3 Combinatorics
Functional Analysis
Metric Geometry
Spectral Theory
Abstract
We study the Banach spectral gap lambda_1(G;X,p) of finite graphs G for pairs (X,p) of Banach spaces and exponents. We define the notion of sphere equivalence between Banach spaces and show a generalization of Matousek's extrapolation for Banach spaces sphere equivalent to uniformly convex ones. As a byproduct, we prove that expanders are automatically expanders with respects to (X,p) for any X sphere equivalent to a uniformly curved Banach space and for any p strictly bigger than 1.
Keywords
Cite
@article{arxiv.1310.4737,
title = {Sphere equivalence, Banach expanders, and extrapolation},
author = {Masato Mimura},
journal= {arXiv preprint arXiv:1310.4737},
year = {2015}
}
Comments
final version,16 pages; 13 pages (v2); 23 pages, no figures, International Mathematics Research Notices, published online, 2014