Sphere Equivalence, Banach Expanders, and Extrapolation
Sphere Equivalence, Banach Expanders, and Extrapolation
复制标题
DOI：
10.1093/imrn/rnu075
复制
发表时间：
2013-10
影响因子：
1
通讯作者：
M. Mimura
中科院分区：
文献类型：
--
作者：
M. Mimura
研究了有限图G的Banach谱间隙λ1(G；X，p)对(X，p)的Banach空间和指数对。定义了Banach空间球面等价的概念，并证明了Banach空间球面的Matousek外推等价于一致凸球面的推广。作为一个副产品，我们证明了对于等价于一致弯曲Banach空间的任何X球面，以及对于任何严格大于1的p，展开器都是关于(X，p)的自动展开器。
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.