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A note on idempotents in finite AW*-factors

Author(s): Gabriel Nagy
Journal: Proc. Amer. Math. Soc. 130 (2002), 1065-1071.
MSC (1991): Primary 46L10; Secondary 46L30
Posted: October 5, 2001
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Abstract: We prove that the value of the quasi-trace on an idempotent element in an AW*-factor of type $\text{II}_1$ is the same as the dimension of its left (or right) support.

References:

[Be]: S. Berberian, Baer -rings, Springer, 1972 MR 46:7294
[BH]: B. Blackadar, D. Handelman, Dimension functions and traces on C*-algebras, J. Funct. Anal. 45 (1982), no. 3, 297-340. MR 83g:46050
[Ha]: U. Haagerup, Quasi-traces on exact C*-algebras are traces, Preprint, 1991
[Ka]: I. Kaplansky, Rings of operators, Benjamin, 1968 MR 39:6092

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Additional Information:

Gabriel Nagy
Affiliation: Department of Mathematics, Kansas State University, Manhattan, Kansas 66506
Email: nagy@math.ksu.edu

DOI: 10.1090/S0002-9939-01-06315-8
PII: S 0002-9939(01)06315-8
Keywords: AW*-algebra, quasi-trace, idempotent, projection, dimension function
Received by editor(s): October 4, 2000
Posted: October 5, 2001
Additional Notes: This work was partially supported by NSF grant DMS 9706858
Communicated by: David R. Larson
Copyright of article: Copyright 2001, American Mathematical Society


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