The Bishop-Phelps-Bollob\'as property for operators from   $\mathcal{C}(K)$ to uniformly convex spaces
  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. 
Sun Kwang Kim and Han Ju Lee
math.FA