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NONCOMPLETE MACKEY TOPOLOGIES ON BANACH SPACES

Part of: Topological linear spaces and related structures Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  05 March 2010

JOSÉ BONET  and
BERNARDO CASCALES
JOSÉ BONET*
Affiliation:
Instituto Universitario de Matemática Pura y Aplicada IUMPA, Universidad Politécnica de Valencia, E-46071 Valencia, Spain (email: jbonet@mat.upv.es)
BERNARDO CASCALES
Affiliation:
Departamento de Matemáticas, Universidad de Murcia, E-30100 Espinardo (Murcia), Spain (email: beca@um.es)
*
✉For correspondence; e-mail: jbonet@mat.upv.es
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Abstract

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Answering a question of W. Arendt and M. Kunze in the negative, we construct a Banach space X and a norm closed weak* dense subspace Y of the dual X′ of X such that X, endowed with the Mackey topology μ(X,Y ) of the dual pair 〈X,Y 〉, is not complete.

Keywords

Banach spacesMackey topologiesnorming subspacesKrein–Smulyan theorem

MSC classification

Secondary: 46B10: Duality and reflexivity 46A03: General theory of locally convex spaces
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 81 , Issue 3 , June 2010 , pp. 409 - 413
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

Footnotes

The research of Bonet was partially supported by FEDER and MEC Project MTM2007-62643 and by GV Prometeo/2008/101. The research of Cascales was supported by FEDER and MEC Project MTM2008-05396 and by Fundación Séneca de la CARM, project 08848/PI/08.

References

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