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The dual of C ps (X)

The dual of C ps (X) This is a study of the dual space of continuous linear functionals on the function space C ps (X) with a natural norm inherited from a larger Banach space. Here ps denotes the pseudocompact-open topology on C(X), the set of all real-valued continuous functions on a Tychonoff space X. The lattice structure and completeness of this dual space have been studied. Since this dual space is inherently related to a space of measures, the measure-theoretic characterization of this dual space has been studied extensively. Due to this characterization, a special kind of topological space, called pz-space, has been studied. Finally the separability of this dual space has been studied. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

The dual of C ps (X)

Positivity , Volume 13 (2) – Oct 4, 2008

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References (38)

Publisher
Springer Journals
Copyright
Copyright © 2008 by Birkhäuser Verlag Basel/Switzerland
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
DOI
10.1007/s11117-008-2186-y
Publisher site
See Article on Publisher Site

Abstract

This is a study of the dual space of continuous linear functionals on the function space C ps (X) with a natural norm inherited from a larger Banach space. Here ps denotes the pseudocompact-open topology on C(X), the set of all real-valued continuous functions on a Tychonoff space X. The lattice structure and completeness of this dual space have been studied. Since this dual space is inherently related to a space of measures, the measure-theoretic characterization of this dual space has been studied extensively. Due to this characterization, a special kind of topological space, called pz-space, has been studied. Finally the separability of this dual space has been studied.

Journal

PositivitySpringer Journals

Published: Oct 4, 2008

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