TY - JOUR
T1 - Sphere equivalence, Banach expanders, and extrapolation
AU - Mimura, Masato
N1 - Publisher Copyright:
© The Author(s) 2014.
PY - 2015
Y1 - 2015
N2 - 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,∞).
AB - 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,∞).
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U2 - 10.1093/imrn/rnu075
DO - 10.1093/imrn/rnu075
M3 - Article
AN - SCOPUS:84941888021
VL - 2015
SP - 4372
EP - 4391
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
SN - 1073-7928
IS - 12
ER -