Berg, I. D.; Sims, Brailey Denseness of operators which attain their numerical radius. (English) Zbl 0561.47004 J. Aust. Math. Soc., Ser. A 36, 130-133 (1984). 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 Cited in 16 Documents 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 Keywords:denseness of operators which attain their numerical radius; numerical range PDFBibTeX XMLCite \textit{I. D. Berg} and \textit{B. Sims}, J. Aust. Math. Soc., Ser. A 36, 130--133 (1984; Zbl 0561.47004)