J. Korean Math. Soc. 2015; 52(1): 177-190
Printed January 1, 2015
https://doi.org/10.4134/JKMS.2015.52.1.177
Copyright © The Korean Mathematical Society.
Marian Nowak
University of Zielona G\'{o}ra
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 $f:X\ps E$ such that $f(X)$ is a relatively compact set in $E$. We establish an integral representation theorem for bounded linear operators $T:C_{rc}(X,E)\ps F$. We characterize continuous operators from $C_{rc}(X,E)$, provided with the strict topologies $\beta_z(X,E)$ $(z=\si,\tau)$ to $F$, in terms of their representing operator-valued measures.
Keywords: spaces of vector-valued continuous functions, strict topologies, vector measures, integration operators
MSC numbers: 46G10, 46A40, 46A70, 28A33
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