Dieudonné operators on C(K,E)



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Bombal Gordón, Fernando and Cembranos, Pilar (1986) Dieudonné operators on C(K,E). Bulletin of the Polish Academy of Sciences. Mathematics, 34 (5-6). pp. 301-305. ISSN 0239-7269

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A Banach space operator is called a Dieudonné operator if it maps weakly Cauchy sequences to weakly convergent sequences. A space E is said to have property (D) if, whenever K is a compact Hausdorff space and T is an operator from C(K,E) into a space F , T is a Dieudonné operator if and only if its representing measure is both strongly additive and has for its values Dieudonné operators from E into F . The purpose of this paper is to show that if E ∗ has the Radon-Nikodým property then E has (D) if and only if E ∗∗ has the Radon-Nikodým property.

Item Type:Article
Uncontrolled Keywords:space of continuous vector valued functions; Dieudonné operator; representing measure; semivariation
Subjects:Sciences > Mathematics > Differential geometry
ID Code:18038
Deposited On:30 Jan 2013 09:54
Last Modified:25 Nov 2019 09:23

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