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