Some classes of continuous operators on spaces of bounded vector-valued continuous functions with the strict topology

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 on x,equipped with the strict topology βσ. we study the relationship between important classes of (βσ,∥ · ∥f) -continuous linear operators t: cb (x,e) →f (strongly bounded,unconditionally converging,weakly completely continuous,completely continuous,weakly compact,nuclear,and strictly singular) and the corresponding operator measures given by riesz representing theorems. some applications concerning the coincidence among these classes of operators are derived. © 2015 marian nowak.