This is an announcement for the paper "Limit theorems for numerical index" by Asuman Guven Aksoy and Grzegorz Lewicki.

Abstract: We improve upon on a limit theorem for numerical index for large classes of Banach spaces including vector valued $\ell_p$-spaces and $\ell_p$-sums of Banach spaces where\ $1\leq p \leq \infty$. We first prove $ n_1( X) = \displaystyle \lim_m n_1( X_m)$ for a modified numerical index $n_1(, ., )$. Later, we establish if a norm on $X$ satisfies the local characterization condition, then $n(X) = \displaystyle\lim_m n(X_m).$ We also present an example of a Banach space where the local characterization condition is satisfied.

Archive classification: math.FA math.OA

Submitted from: aaksoy@cmc.edu

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1106.4822

or

http://arXiv.org/abs/1106.4822