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On the Pták homomorphism theorem

Part of: General theory of linear operators Topological linear spaces and related structures

Published online by Cambridge University Press:  09 April 2009

B. Rodrigues
B. Rodrigues
Affiliation:
Department of Mathematical Sciences, Loyola UniversityNew Orleans, Louisiana 70118, U.S.A.
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Abstract

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In this note, a brief and accessible proof is given of an extension of the Pták homomorphism theorem to a larger class of spaces—spaces that are not necessarily assumed to be locally convex. This is done by first proving a counterpart of the Bourbaki-Grothendieck homomophism theorem for the non-locally-convex case. Our presentation utilizes the simplifying properties of seminorms.

Keywords

semi-barrelled spacebarrelled spacesemi-B-completeB-completequotient seminormadequate mapsmall adjointsemi-openweakly opennearly semi-opennearly semi-continuous.

MSC classification

Secondary: 46A30: Open mapping and closed graph theorems; completeness (including $B$-, $B_r$-completeness) 47A05: General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 47 , Issue 2 , October 1989 , pp. 322 - 333
Copyright
Copyright © Australian Mathematical Society 1989

References

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