• Journal of the Korean Mathematical Society
• /
• v.52 no.1
• /
• pp.177-190
• /
• 2015

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.

• Bulletin of the Korean Mathematical Society
• /
• v.45 no.4
• /
• pp.681-687
• /
• 2008

We give a characterization of trans-separability for the function spaces ($C_b(X,\;E)$, $\beta$), (C(X, E), k) and ($C_b(X,\;E)$, u) in the case of E any general topological vector space.