The Bishop-Phelps-Bollob\'as property for operators from $\mathcal{C}(K)$ to uniformly convex spaces

TL;DR

This paper proves that the pair of spaces consisting of continuous functions on a compact Hausdorff space and uniformly convex spaces has the Bishop-Phelps-Bollobás property for operators, extending the understanding of operator approximation.

Contribution

It establishes the Bishop-Phelps-Bollobás property for operators from $C(K)$ to uniformly convex spaces, a significant extension in the theory of operator approximation.

Findings

The pair $(C(K),X)$ has the Bishop-Phelps-Bollobás property for operators.

The result applies when $K$ is a compact Hausdorff space and $X$ is uniformly convex.

This advances the understanding of operator approximation in functional analysis.

Abstract

We show that the pair $(C(K),X)$ has the Bishop-Phelps-Bolloba\'as property for operators if $K$ is a compact Hausdorff space and $X$ is a uniformly convex space.