Linear operators on the space of bounded continuous functions with strict topologies

Let X be a completely regular Hausdorff space, and let C (b) (X) denote the Banach space of all real-valued bounded continuous functions on X. We study linear operators from C (b) (X) provided with the strict topology beta (sigma) to a Banach space (E, parallel to center dot parallel to(E)). In particular, we derive a Yosida-Hewitt type decomposition for weakly compact operator from C-b (X) to E.