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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Bicommutants of reduced unbounded operator algebras


Authors: Fabio Bagarello, Atsushi Inoue and Camillo Trapani
Journal: Proc. Amer. Math. Soc. 137 (2009), 3709-3716
MSC (2000): Primary 47L60
Published electronically: June 29, 2009
MathSciNet review: 2529878
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Abstract: The unbounded bicommutant $ (\mathfrak{M}_{E'})''_{\mathrm{wc}}$ of the reduction of an O*-algebra $ \mathfrak{M}$ via a given projection $ E'$ weakly commuting with $ \mathfrak{M}$ is studied, with the aim of finding conditions under which the reduction of a GW*-algebra is a GW*-algebra itself. The obtained results are applied to the problem of the existence of conditional expectations on O*-algebras.


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Additional Information

Fabio Bagarello
Affiliation: Dipartimento di Metodi e Modelli Matematici, Facoltà d’Ingegneria, Università di Palermo, I-90128 Palermo, Italy
Email: bagarell@unipa.it

Atsushi Inoue
Affiliation: Department of Applied Mathematics, Fukuoka University, Fukuoka 814-0180, Japan
Email: a-inoue@fukuoka-u.ac.jp

Camillo Trapani
Affiliation: Dipartimento di Matematica ed Applicazioni, Università di Palermo, I-90123 Palermo, Italy
Email: trapani@unipa.it

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10023-0
PII: S 0002-9939(09)10023-0
Received by editor(s): September 9, 2008
Published electronically: June 29, 2009
Additional Notes: This work was supported by CORI, Università di Palermo.
Communicated by: Marius Junge
Article copyright: © Copyright 2009 American Mathematical Society