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STRICT TOPOLOGIES AND OPERATORS ON SPACES OF VECTOR-VALUED CONTINUOUS FUNCTIONS
Nowak, Marian Korean Mathematical Society 2015 대한수학회지 Vol.52 No.1
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.
STRICT TOPOLOGIES AND OPERATORS ON SPACES OF VECTOR-VALUED CONTINUOUS FUNCTIONS
Marian Nowak 대한수학회 2015 대한수학회지 Vol.52 No.1
Let X be a completely regular Hausdorff space, and E and F be Banach spaces. Let Crc(X,E) be the Banach space of all continuous functions f : X → E such that f(X) is a relatively compact set in E. We establish an integral representation theorem for bounded linear op- erators T : Crc(X, E) → F. We characterize continuous operators from Crc(X,E), provided with the strict topologies βz(X,E) (z = σ, τ) to F, in terms of their representing operator-valued measures.