Bishop-Phelps-Bollob\'as property for bilinear forms on spaces of continuous functions

TL;DR

This paper proves that the Bishop-Phelps-Bollobás property applies to bilinear forms on spaces of continuous functions over locally compact Hausdorff spaces, extending the theorem's applicability.

Contribution

It establishes the Bishop-Phelps-Bollobás property for bilinear forms on C_0 spaces over arbitrary locally compact Hausdorff spaces, broadening previous results.

Findings

Bishop-Phelps-Bollobás property holds for bilinear forms on C_0 spaces.

The result applies to arbitrary locally compact Hausdorff spaces.

The theorem extends known cases to more general topological spaces.

Abstract

It is shown that the Bishop-Phelps-Bollob\'as theorem holds for bilinear forms on the complex $C_0(L_1)\times C_0(L_2)$ for arbitrary locally compact topological Hausdorff spaces $L_1$ and $L_2$.