Operators on spaces of bounded vector-valued continuous functions with strict topologies

Let x be a completely regular hausdorff space,and let (e,|·|e) and (f,|·|f) be banach spaces. let cb(x,e) be the space of all e-valued bounded,continuous functions defined on x,equipped with the strict topologies βz,where z=σ,∞,p,τ,t. general integral representation theorems of (βz,|·|f)-continuous linear operators t:cb(x,e)→f with respect to the corresponding operator-valued measures are established. strongly bounded and (βz,|·|f)-continuous operators t:cb(x,e)→f are studied. we extend to the completely regular setting some classical results concerning operators on the spaces c(x,e) and co(x,e),where x is a compact or a locally compact space. © 2015 marian nowak.