Han Ju Lee

On the Bishop-Phelps-Bollobás Property for Numerical Radius

We study the Bishop-Phelps-Bollobas property for numerical radius (in short, BPBp-nu) and find sufficient conditions for Banach spaces to ensure the BPBp-nu. Among other results, we show that -spaces have this property for every measure μ. On the other hand, we show that every infinite-dimensional separable Banach space can be renormed to fail the BPBp-nu. In particular, this shows that the Radon-Nikodým property (even reflexivity) is not enough to get BPBp-nu.

The Bishop–Phelps–Bollobás property for operators from C(K) to uniformly convex spaces

Abstract We show that the pair ( C ( K ) , X ) has the Bishop–Phelps–Bollobas property for operators if K is a compact Hausdorff space and X is a uniformly convex space.

Bishop–Phelps–Bollobás property for bilinear forms on spaces of continuous functions

It is shown that the Bishop–Phelps–Bollobás theorem holds for bilinear forms on the complex

The Bishop–Phelps–Bollobás property for operators between spaces of continuous functions

C_0(L_1)\times C_0(L_2)

The Bishop-Phelps-Bollobás property for bilinear forms and polynomials

C0(L1)×C0(L2) for arbitrary locally compact topological Hausdorff spaces

Polynomial numerical indices of Banach spaces with 1-unconditional bases

L_1