Power type ξ-asymptotically uniformly smooth norms

2016/08/12 by Causey, Ryan M
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1608.03666

Abstract

We extend a precise renorming result of Godefroy, Kalton, and Lancien regarding asymptotically uniformly smooth norms of separable Banach spaces with Szlenk index ω. For every ordinal ξ, we characterize the operators, and therefore the Banach spaces, which admit a ξ-asymptotically uniformly smooth norm with power type modulus and compute for those operators the best possible exponent in terms of the values of Sz_ξ(⋅, ε). We also introduce the ξ-Szlenk power type and investigate ideal and factorization properties of classes associated with the ξ-Szlenk power type.

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