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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Bicommutants of reduced unbounded operator algebras
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by Fabio Bagarello, Atsushi Inoue and Camillo Trapani
Proc. Amer. Math. Soc. 137 (2009), 3709-3716
DOI: https://doi.org/10.1090/S0002-9939-09-10023-0
Published electronically: June 29, 2009

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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Bibliographic 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