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Boolean algebras of projections in (DF)-and (LF)-spaces

Published online by Cambridge University Press:  17 April 2009

J. Bonet  and
W. J. Ricker
J. Bonet
Affiliation:
Dpto. Matematica Aplicada, Universidad Politecnica de Valencia, E-46071 Valencia, Spain
W. J. Ricker
Affiliation:
Math.-Geogr. Fakultät, Katholische Universität Eichstätt-Ingolstadt, D-85072 Eichstätt, Germany
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Abstract

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Conditions are presented which ensure that an abstractly σ-complete Boolean algebra of projections on a (DF)-space or on an (LF)-space is necessarily equicontinuous and/or the range of a spectral measure. This is an extension, to a large and important class of locally convex spaces, of similar and well known results due to W. Bade (respectively, B. Walsh) in the setting of normed (respectively metrisable) spaces.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 67 , Issue 2 , April 2003 , pp. 297 - 303
Copyright
Copyright © Australian Mathematical Society 2003

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