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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Integral operators on spaces of continuous vector-valued functions


Author: Paulette Saab
Journal: Proc. Amer. Math. Soc. 111 (1991), 1003-1013
MSC: Primary 47B38; Secondary 46E40, 46G10, 47B10
DOI: https://doi.org/10.1090/S0002-9939-1991-1039263-5
MathSciNet review: 1039263
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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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DOI: https://doi.org/10.1090/S0002-9939-1991-1039263-5
Article copyright: © Copyright 1991 American Mathematical Society

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