STRICT TOPOLOGIES AND OPERATORS ON SPACES OF VECTOR-VALUED CONTINUOUS FUNCTIONS

• Published in: Journal of the Korean Mathematical Society Vol. 52; no. 1; pp. 177 - 190
• Main Author: Nowak, Marian
• Format: Journal Article
• Language: Korean
• Published: 2015
• Subjects: vector measures; strict topologies; integration operators; spaces of vector-valued continuous functions
• ISSN: 0304-9914

Let X be a completely regular Hausdorff space, and E and F be Banach spaces. Let $C_{rc}(X,E)$ be the Banach space of all continuous functions $f:X{\rightarrow}E$ such that f(X) is a relatively compact set in E. We establish an integral representation theorem for bounded linear operators $T:C_{rc}(X,E){\rightarrow}F$. We characterize continuous operators from $C_{rc}(X,E)$, provided with the strict topologies ${\beta}_z(X,E)$ ($z={\sigma},{\tau}$) to F, in terms of their representing operator-valued measures.