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

Maria Acosta, Julio Becerra, Yun Sung Choi, Maciej Ciesielski, Sun Kwang Kim, Han Ju Lee, Mary Lilian Lourenço, Miguel Martin

Published 2013-06-28, updated 2013-07-22Version 2

We show that the space of bounded and linear operators between spaces of continuous functions on compact Hausdorff topological spaces has the Bishop-Phelps-Bollob\'as property. A similar result is also proved for the class of compact operators from the space of continuous functions vanishing at infinity on a locally compact and Hausdorff topological space into a uniformly convex space, and for the class of compact operators from a Banach space into a predual of an $L_1$-space.