Sphere equivalence, Banach expanders, and extrapolation

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6 Citations (Scopus)

Abstract

We study the Banach spectral gap λ1(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 Matoušek's extrapolation for Banach spaces sphere equivalent to uniformly convex ones. As a byproduct, we prove that expanders are automatically expanders with respect to (X, p) for any X sphere equivalent to a uniformly curved Banach space and for any pε(1,∞).

Original languageEnglish
Pages (from-to)4372-4391
Number of pages20
JournalInternational Mathematics Research Notices
Volume2015
Issue number12
DOIs
Publication statusPublished - 2015

ASJC Scopus subject areas

  • Mathematics(all)

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