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Journal of Function Spaces
Volume 2015 (2015), Article ID 796753, 13 pages
http://dx.doi.org/10.1155/2015/796753
Research Article

Some Classes of Continuous Operators on Spaces of Bounded Vector-Valued Continuous Functions with the Strict Topology

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

Received 28 October 2014; Accepted 2 January 2015

Academic Editor: Luisa Di Piazza

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 on , equipped with the strict topology . We study the relationship between important classes of -continuous linear operators (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.