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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

Atsushi Inoue
Affiliation: Department of Applied Mathematics, Fukuoka University, Fukuoka 814-0180, Japan

Camillo Trapani
Affiliation: Dipartimento di Matematica ed Applicazioni, Università di Palermo, I-90123 Palermo, Italy

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