Denseness of Operators Whose Second Adjoints Attain Their Numerical Radii

Maria D. Acosta, Rafael Paya
1989 Proceedings of the American Mathematical Society  
We show that for any Banach space the set of (bounded linear) operators whose second adjoints attain their numerical radii is norm-dense in the space of all operators. In particular, the numerical radius attaining operators on a reflexive space are dense. B. Sims, paralleling the investigations by J. Lindenstrauss on norm attaining operators, raised the question of the norm denseness of numerical radius attaining operators. To date, only partial answers to this question have been given. Berg
more » ... been given. Berg and Sims [1] got an affirmative answer for uniformly convex spaces.
doi:10.2307/2046740 fatcat:4fdn4gounjhupjixwvyast2bs4