Operators on Spaces of Bounded Vector-Valued Continuous Functions with Strict Topologies. (6th April 2015)

• Record Type: Journal Article
• Authors: Nowak, Marian
• Other Names: Banaś Józef Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2015(2015)
• Publication Date: 2015-04-06
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2015/407521
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : Let X be a completely regular Hausdorff space, and let( E, ‖ · ‖ E ) and( F, ‖ · ‖ F ) be Banach spaces. Let C b ( X, E ) be the space of all E -valued bounded, continuous functions defined on X, equipped with the strict topologies β z, where z = σ, ∞, p, τ, t . General integral representation theorems of( β z, ‖ · ‖ F ) -continuous linear operators T : C b ( X, E ) → F with respect to the corresponding operator-valued measures are established. Strongly bounded and( β z, ‖ · ‖ F ) -continuous operators T : C b ( X, E ) → F are studied. We extend to "the completely regular setting" some classical results concerning operators on the spaces C ( X, E ) and C o ( X, E ), where X is a compact or a locally compact space.