This is an announcement for the paper "Best approximation in numerical radius" by Asuman Guven Aksoy and Grzegorz Lewicki.
Abstract: Let $X$ be a reflexive Banach space. In this paper we give a necessary and sufficient condition for an operator $T\in \mathcal{K}(X)$ to have the best approximation in numerical radius from the convex subset $\mathcal{U} \subset \mathcal{K}(X),$ where $\mathcal{K}(X)$ denotes the set of all linear, compact operators from $X$ into $X.$ We will also present an application to minimal extensions with respect to the numerical radius. In particular some results on best approximation in norm will be generalized to the case of the numerical radius.
Archive classification: math.FA
Remarks: 13 pages
Submitted from: aaksoy@cmc.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1007.2205
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