Limit theorems for the numerical index

作者：Aksoy Asuman Gueven^*; Lewicki Grzegorz

来源：Journal of Mathematical Analysis and Applications, 2013, 398(1): 296-302.

DOI：10.1016/j.jmaa.2012.08.055

• Numerical index
• Numerical radius
• Local characterization condition

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 %26lt;= p %26lt; 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.

• 出版日期2013-2-1