Bicommutants of reduced unbounded operator algebras
HTML articles powered by AMS MathViewer
- 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
- PDF | 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
- Jacques Dixmier, von Neumann algebras, North-Holland Mathematical Library, vol. 27, North-Holland Publishing Co., Amsterdam-New York, 1981. With a preface by E. C. Lance; Translated from the second French edition by F. Jellett. MR 641217
- Atsushi Inoue, On a class of unbounded operator algebras, Pacific J. Math. 65 (1976), no. 1, 77–95. MR 512382
- Atsushi Inoue, Hidekazu Ogi, and Mayumi Takakura, Conditional expectations for unbounded operator algebras, Int. J. Math. Math. Sci. , posted on (2007), Art. ID 80152, 22. MR 2320785, DOI 10.1155/2007/80152
- Atsushi Inoue, M. Takakura, and H. Ogi, Unbounded conditional expectations for $O^*$-algebras, Topological algebras and applications, Contemp. Math., vol. 427, Amer. Math. Soc., Providence, RI, 2007, pp. 225–234. MR 2326358, DOI 10.1090/conm/427/08155
- Robert T. Powers, Self-adjoint algebras of unbounded operators, Comm. Math. Phys. 21 (1971), 85–124. MR 283580
- Konrad Schmüdgen, Unbounded operator algebras and representation theory, Operator Theory: Advances and Applications, vol. 37, Birkhäuser Verlag, Basel, 1990. MR 1056697, DOI 10.1007/978-3-0348-7469-4
- Masamichi Takesaki, Conditional expectations in von Neumann algebras, J. Functional Analysis 9 (1972), 306–321. MR 0303307, DOI 10.1016/0022-1236(72)90004-3
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