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Denseness of operators which attain their numerical radius. (English) Zbl 0561.47004

The authors show that each (bounded linear) operator T on a uniformly convex Banach space X has a compact operator K of arbitrary small norm such that \(T+K\) attains its numerical radius \(\nu (T+K)\) (that is, some x in X and some state f on X attain \(\nu (T+K))\).
Reviewer: Y.Kato

MSC:

47A12 Numerical range, numerical radius
47A55 Perturbation theory of linear operators
47B06 Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
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