Bicommutants of reduced unbounded operator algebras
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- by Fabio Bagarello, Atsushi Inoue and Camillo Trapani PDF
- Proc. Amer. Math. Soc. 137 (2009), 3709-3716 Request permission
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.References
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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
- 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
- © Copyright 2009 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 137 (2009), 3709-3716
- MSC (2000): Primary 47L60
- DOI: https://doi.org/10.1090/S0002-9939-09-10023-0
- MathSciNet review: 2529878