Representing conditional expectations as elementary operators
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- by Rajesh Pereira PDF
- Proc. Amer. Math. Soc. 134 (2006), 253-258 Request permission
Abstract:
Let $\mathcal {A}$ be a $C^{*}$-algebra and let $\mathcal {B}$ be a $C^{*}$-subalgebra of $\mathcal {A}$. We call a linear operator from $\mathcal {A}$ to $\mathcal {B}$ an elementary conditional expectation if it is simultaneously an elementary operator and a conditional expectation of $\mathcal {A}$ onto $\mathcal {B}$. We give necessary and sufficient conditions for the existence of a faithful elementary conditional expectation of a prime unital $C^{*}$-algebra onto a subalgebra containing the identity element. We give a description of all faithful elementary conditional expectations. We then use these results to give necessary and sufficient conditions for certain conditional expectations to be index-finite (in the sense of Watatani) and we derive an inequality for the index.References
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Additional Information
- Rajesh Pereira
- Affiliation: Department of Mathematics and Statistics, University of Saskatchewan, 106 Wiggins Road, Saskatoon, Saskatchewan, Canada S7N 5E6
- Email: rjxpereira@yahoo.com
- Received by editor(s): September 1, 2004
- Published electronically: June 14, 2005
- Communicated by: David R. Larson
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 253-258
- MSC (2000): Primary 46L05, 47B47
- DOI: https://doi.org/10.1090/S0002-9939-05-08031-7
- MathSciNet review: 2170565