A characterization of nuclear operators on spaces of vector-valued continuous functions with the strict topology

Stochmal, Juliusz

doi:10.1090/proc/16805

A characterization of nuclear operators on spaces of vector-valued continuous functions with the strict topology
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by Juliusz Stochmal;

Proc. Amer. Math. Soc. 152 (2024), 2999-3010

DOI: https://doi.org/10.1090/proc/16805

Published electronically: May 21, 2024

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Abstract:

Let $X$ be a completely regular Hausdorff space, let $E$ and $F$ denote Banach spaces. Let $C_b(X,E)$ denote the space of $E$-valued bounded continuous functions on $X$ and let $\beta$ be the strict topology on this space. We establish the relationship between nuclear operators $T:C_b(X,E)\rightarrow F$ between the locally convex space $(C_b(X,E),\beta )$ and the Banach space $F$ and their representing operator-valued Borel measures.

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