Representing conditional expectations as elementary operators

Author:
Rajesh Pereira

Journal:
Proc. Amer. Math. Soc. **134** (2006), 253-258

MSC (2000):
Primary 46L05, 47B47

Published electronically:
June 14, 2005

MathSciNet review:
2170565

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a -algebra and let be a -subalgebra of . We call a linear operator from to an elementary conditional expectation if it is simultaneously an elementary operator and a conditional expectation of onto . We give necessary and sufficient conditions for the existence of a faithful elementary conditional expectation of a prime unital -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.

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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

DOI:
http://dx.doi.org/10.1090/S0002-9939-05-08031-7

Keywords:
Prime $C^{*}$-algebras,
conditional expectations,
elementary operators,
index finite type,
minimal conditional expectation

Received by editor(s):
September 1, 2004

Published electronically:
June 14, 2005

Communicated by:
David R. Larson

Article copyright:
© Copyright 2005
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.