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Transactions of the American Mathematical Society

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Some locally convex spaces of continuous vector-valued functions over a completely regular space and their duals

Author: A. Katsaras
Journal: Trans. Amer. Math. Soc. 216 (1976), 367-387
MSC: Primary 46E10
MathSciNet review: 0390733
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Abstract: The strict, superstrict and the $ {\beta _F}$ topologies are defined on a space A of continuous functions from a completely regular space into a Banach space E. Properties of these topologies are discussed and the corresponding dual spaces are identified with certain spaces of operator-valued measures. In case E is a Banach lattice, A becomes a lattice under the pointwise ordering and the strict and superstrict duals of A coincide with the spaces of all $ \tau $-additive and all $ \sigma $-additive functionals on A respectively.

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Keywords: Locally convex spaces, strict topology, mixed topology, operator-valued measures, $ \sigma $-additive functionals, $ \tau $-additive functionals
Article copyright: © Copyright 1976 American Mathematical Society

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