Denseness of operators whose second adjoints attain their numerical radii
Denseness of operators whose second adjoints attain their numerical radii
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 …