Integral operators on spaces of continuous vector-valued functions

Saab, Paulette

doi:10.1090/S0002-9939-1991-1039263-5

Integral operators on spaces of continuous vector-valued functions
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Proc. Amer. Math. Soc. 111 (1991), 1003-1013 Request permission

Abstract:

Let $X$ be a compact Hausdorff space, let $E$ be a Banach space, and let $C(X,E)$ stand for the Banach space of $E$-valued continuous functions on $X$ under the uniform norm. In this paper we characterize integral operators (in the sense of Grothendieck) on $C(X,E)$ spaces in terms of their representing vector measures. This is then used to give some applications to nuclear operators on $C(X,E)$ spaces.

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