This is an announcement for the paper "Sphere equivalence, Banach expanders, and extrapolation" by Masato Mimura. 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 introduce the notion of sphere equivalence between Banach spaces, and study behavior of lambda_1(G;X,p) for fixed p in terms of this equivalence. We further study behavior of lambda_1(G;X,p) for fixed X. As a byproduct, we show a generalization of Matousek's extrapolation to that for any Banach space which is sphere equivalent to a uniformly convex Banach space. We as well prove that expanders are expanders with respects to (X,p) for any X sphere equivalent to a uniformly curved Banach space and for any finite p strictly bigger than 1. Archive classification: math.GR math.CO math.FA math.MG Remarks: 23 pages, no figure Submitted from: mimura-mas@m.tohoku.ac.jp The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1310.4737 or http://arXiv.org/abs/1310.4737