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Some Locally Convex Spaces of Continuous Vector-Valued Functions Over a Completely Regular Space and Their Duals

A. Katsaras
Transactions of the American Mathematical Society
Vol. 216 (Feb., 1976), pp. 367-387
DOI: 10.2307/1997705
Stable URL: http://www.jstor.org/stable/1997705
Page Count: 21
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Some Locally Convex Spaces of Continuous Vector-Valued Functions Over a Completely Regular Space and Their Duals
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Abstract

The strict, superstrict and the βF 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 τ-additive and all σ-additive functionals on A respectively.

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