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Journal of Function Spaces
Volume 2015, Article ID 407521, 12 pages
http://dx.doi.org/10.1155/2015/407521
Research Article

Operators on Spaces of Bounded Vector-Valued Continuous Functions with Strict Topologies

Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Ulica Szafrana 4A, 65-516 Zielona Góra, Poland

Received 30 June 2014; Accepted 26 August 2014

Academic Editor: Józef Banaś

Copyright © 2015 Marian Nowak. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let be a completely regular Hausdorff space, and let and be Banach spaces. Let be the space of all -valued bounded, continuous functions defined on , equipped with the strict topologies , where . General integral representation theorems of -continuous linear operators with respect to the corresponding operator-valued measures are established. Strongly bounded and -continuous operators are studied. We extend to “the completely regular setting” some classical results concerning operators on the spaces and , where is a compact or a locally compact space.