Best Approximation in Numerical Radius

Details Best Approximation in Numerical Radius Best Approximation in Numerical Radius

2010-07-13

arxiv.org/abs/1007.2205v1

Mathematics

Functional Analysis

13 pages

Scientific paper

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.

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