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The strong closure of Boolean algebras of projections in Banach spaces

Part of: Normed linear spaces and Banach spaces; Banach lattices Linear spaces and algebras of operators

Published online by Cambridge University Press:  09 April 2009

J. Diestel  and
W. J. Ricker
J. Diestel
Affiliation:
Department of Mathematical Sciences, Kent State University, P.O. Box 5190, Kent OH 44242-0001, USA e-mail: diestelj@aol.com
W. J. Ricker
Affiliation:
Math.-Geogr. Fakultät, Katholische Universität, Eichstätt-Ingolstadt, D-85072 Eichstätt, Germany e-mail: werner.ricker@ku-eichstaett.de
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Abstract

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This note improves two previous results of the second author. They turn out to be special cases of our main theorem which states: A Banach space X has the property that the strong closure of every abstractly σ-complete Boolean algebra of projections in X is Bade complete if and only if X does not contain a copy of the sequence space ℓ∞.

MSC classification

Secondary: 46B25: Classical Banach spaces in the general theory 47L10: Algebras of operators on Banach spaces and other topological linear spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 77 , Issue 3 , December 2004 , pp. 365 - 370
Copyright
Copyright © Australian Mathematical Society 2004

References

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