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A characterization of the second dual of $ C\sb 0(S,A)$

Authors: Stephen T. L. Choy and James C. S. Wong
Journal: Proc. Amer. Math. Soc. 120 (1994), 203-211
MSC: Primary 46E40; Secondary 46G99, 46J10
MathSciNet review: 1163330
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Abstract: Let $ S$ be a locally compact Hausdorff space, and let $ A$ be a Banach space. The space of the continuous functions from $ S$ to $ A$ vanishing at infinity is denoted by $ {C_0}(S,A)$. Let $ MW(S,{A^{\ast}})$ be the space of the representing measures of all the bounded linear functionals on $ {C_0}(S,A)$. For $ \mu \in MW(S,{A^{\ast}})$ let

$\displaystyle {L_\infty }(\vert\mu \vert,{A^{{\ast}{\ast}}},{A^{\ast}}) = \{ f:... ...){x^{\ast}} \in {L_\infty }(\vert\mu \vert)\forall {x^{\ast}} \in {A^{\ast}}\}.$

The second dual of $ {C_0}(S,A)$ is characterized in the general case by means of certain elements in the product linear space $ \prod {\{ {L_\infty }(\vert\mu \vert,{A^{{\ast}{\ast}}},{A^{\ast}}):\mu \in MW(S,{A^{\ast}})\} } $.

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Keywords: Second dual, vector-valued function space, Bochner integrable functions
Article copyright: © Copyright 1994 American Mathematical Society

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