Limit theorems for the numerical index

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:398

Article

Aksoy, Asuman Gueven¹  Lewicki, Grzegorz² 

[1] Claremont McKenna Coll, Dept Math, Claremont, CA 91711 USA

[2] Jagiellonian Univ, Dept Math, PL-30348 Krakow, Poland

关键词: Numerical index;    Numerical radius;    Local characterization condition;   

DOI  :  10.1016/j.jmaa.2012.08.055

来源: Elsevier

【 摘 要 】

We improve on a limit theorem (see Martin et al. (2011) [13], Th. 5.1) for numerical index n(.) for large classes of Banach spaces including vector valued l(p)-spaces and l(p)-sums of Banach spaces where 1 <= p < infinity. We introduce two conditions on a Banach space X, a local characterization condition (LCC) and a global characterization condition (GCC). We prove that if a norm on X satisfies the (LCC), then n(X) = lim(m) n(X-m). An analogous result, in which N will be replaced by a directed, infinite set S will be proved for X satisfying the (GCC). We also present examples of Banach spaces satisfying the above mentioned conditions. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free