The Bishop-Phelps-Bollobás property for operators on $C(K)$

Maria D. Acosta

Published 2014-05-25, updated 2014-06-16Version 2

We provide a version for operators of the Bishop-Phelps-Bollob\'{a}s Theorem when the domain space is the complex space $C_0(L)$. In fact we prove that the pair $(C_0(L), Y)$ satisfies the Bishop-Phelps-Bollob\'{a}s property for operators for every Hausdorff locally compact space $L$ and any $\mathbb{C}$-uniformly convex space. As a consequence, this holds for $Y= L_p (\mu)$ ($1 \le p < \infty $).