Vector measures and strict topologies

Let X be a completely regular Hausdorff space and C b ( X ) be the space of all real-valued bounded continuous functions on X, endowed with the strict topology β σ . We study topological properties of continuous and weakly compact operators from C b ( X ) to a locally convex Hausdorff space in terms of their representing vector measures. In particular, Alexandrov representation type theorems are derived. Moreover, a Yosida–Hewitt type decomposition for weakly compact operators on C b ( X ) is given.