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A generalisation of Mackey's theorem and the uniform boundedness principle

Published online by Cambridge University Press:  17 April 2009

Charles Swartz
Charles Swartz
Affiliation:
Department of Mathematical SciencesNew Mexico State UniversityLas Cruces, New Mexico 88003United States of America
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Abstract

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We construct a locally convex topology which is stronger than the Mackey topology but still has the same bounded sets as the Mackey topology. We use this topology to give a locally convex version of the Uniform Bouudedness Principle which is valid without any completeness or barrelledness assumptions.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 40 , Issue 1 , August 1989 , pp. 123 - 128
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Antosik, P. and Swartz, C., Matrix Methods in Analysis: Lecture Notes in Math. 1113 (Springer-Verlag, Berlin, 1985).CrossRefGoogle Scholar
[2]Köthe, G., Topological Vector Spaces I (Springer-Verlag, Berlin, 1983).CrossRefGoogle Scholar