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Polar locally convex topologies and Attouch-Wets convergence

Published online by Cambridge University Press:  17 April 2009

Gerald Beer
Gerald Beer
Affiliation:
Department of Mathematics, California State University, Los Angeles Los Angeles, CA 90032, United States of America
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Abstract

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Let X be a Hausdorff locally convex space. We show that convergence of a net of continuous linear functionals on X with respect to a given polar topology on its continuous dual X′ can be explained in terms of the convergence of the corresponding net of its graphs in X × R, and the corresponding net of level sets at a fixed height in X, with respect to a natural generalisation of Attouch-Wets convergence in normable spaces.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 46 , Issue 1 , August 1992 , pp. 33 - 46
Copyright
Copyright © Australian Mathematical Society 1992

References

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