Acosta, María D. Denseness of numerical radius attaining operators. Renorming and embedding results. (English) Zbl 0725.47004 Indiana Univ. Math. J. 40, No. 3, 903-914 (1991). We prove that a strong geometrical condition (the unit ball is the balanced convex hull of a uniformly strongly exposed set), introduced by J. Lindenstrauss to deal with norm-attaining operators, is also sufficient for the denseness of numerical radius attaining operators. As a consequence, we show that every WCG Banach space can be equivalently renormed in such a way that the denseness of the numerical radius attaining operators is satisfied. We also obtain that every Banach space X is linearly isometric to a 1-complemented subspace of a Banach space Y with the same density character and such that the numerical radius attaining operators on Y are dense. Reviewer: M.D.Acosta (Granada) Cited in 6 Documents MSC: 47A12 Numerical range, numerical radius 46B10 Duality and reflexivity in normed linear and Banach spaces 46B03 Isomorphic theory (including renorming) of Banach spaces Keywords:weakly compactly generated; unit ball is the balanced convex hull of a uniformly strongly exposed set; norm-attaining operators; denseness of numerical radius attaining operators; WCG Banach space; 1-complemented subspace of a Banach space; same density character PDFBibTeX XMLCite \textit{M. D. Acosta}, Indiana Univ. Math. J. 40, No. 3, 903--914 (1991; Zbl 0725.47004) Full Text: DOI