A note on idempotents in finite AW*-factors
HTML articles powered by AMS MathViewer
- by Gabriel Nagy PDF
- Proc. Amer. Math. Soc. 130 (2002), 1065-1071 Request permission
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
- S. K. Berberian, The regular ring of a finite Baer $^{\ast }$-ring, J. Algebra 23 (1972), 35–65. MR 308179, DOI 10.1016/0021-8693(72)90044-0
- Bruce Blackadar and David Handelman, Dimension functions and traces on $C^{\ast }$-algebras, J. Functional Analysis 45 (1982), no. 3, 297–340. MR 650185, DOI 10.1016/0022-1236(82)90009-X
- U. Haagerup, Quasi-traces on exact C*-algebras are traces, Preprint, 1991
- Irving Kaplansky, Rings of operators, W. A. Benjamin, Inc., New York-Amsterdam, 1968. MR 0244778
Additional Information
- Gabriel Nagy
- Affiliation: Department of Mathematics, Kansas State University, Manhattan, Kansas 66506
- Email: nagy@math.ksu.edu
- Received by editor(s): October 4, 2000
- Published electronically: October 5, 2001
- Additional Notes: This work was partially supported by NSF grant DMS 9706858
- Communicated by: David R. Larson
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 1065-1071
- MSC (1991): Primary 46L10; Secondary 46L30
- DOI: https://doi.org/10.1090/S0002-9939-01-06315-8
- MathSciNet review: 1873780