Some Classes of Continuous Operators on Spaces of Bounded Vector-Valued Continuous Functions with the Strict Topology. (22nd February 2015) - Nowak, Marian
Abstract : LetX be a completely regular Hausdorff space and letE, · E and( F, · F ) be Banach spaces. LetC b ( X, E ) be the space of allE -valued bounded, continuous functions onX, equipped with the strict topologyβ σ . We study the relationship between important classes of( β σ, · F ) -continuous linear operatorsT : C b ( 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.