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,∞).
ASJC Scopus subject areas
- 数学 (全般)