POWER TYPE ξ-ASYMPTOTICALLY UNIFORMLY SMOOTH NORMS

被引:10
作者
Causey, R. M. [1 ]
机构
[1] Miami Univ, Dept Math, Oxford, OH 45056 USA
关键词
Asplund operators; asymptotic uniform smoothness; asymptotic uniform convexity; renorming; SZLENK INDEX; WEAK-ASTERISK;
D O I
10.1090/tran/7336
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We extend a precise renorming result of Godefroy, Kalton, and Lancien regarding asymptotically uniformly smooth norms of separable Banach spaces with Szlenk index omega. For every ordinal xi, we characterize the operators, and therefore the Banach spaces, which admit xi-asymptotically uniformly smooth norm with power type modulus and compute for those operators the best possible exponent in terms of the values of Sz(xi)(., epsilon). We also introduce the xi-Szlenk power type and investigate ideal and factorization properties of classes associated with the xi-Szlenk power type.
引用
收藏
页码:1509 / 1546
页数:38
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