On characterizations of commutativity of C$^*$-algebras
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- by Guoxing Ji and Jun Tomiyama PDF
- Proc. Amer. Math. Soc. 131 (2003), 3845-3849 Request permission
Abstract:
We give three kinds of characterizations of the commutativity of C$^*$- algebras. The first is the one from operator monotone property of functions regarded as the nonlinear version of Stinespring theorem, the second one is the characterization of commutativity of local type from expansion formulae of related functions and the third one is of global type from multiple positivity of those nonlinear positive maps induced from functions.References
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Additional Information
- Guoxing Ji
- Affiliation: College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, People’s Republic of China
- Email: gxji@snnu.edu.cn
- Jun Tomiyama
- Affiliation: Department of Mathematics, Japan Women’s University, Tokyo, Japan
- Email: tomiyama@jwu.ac.jp
- Received by editor(s): March 2, 2001
- Received by editor(s) in revised form: July 29, 2002
- Published electronically: March 25, 2003
- Additional Notes: This research was supported by the Excellent Young Teachers Program of MOE, P.R.C. and by the National Natural Science Foundation of China (No.10071047)
- Communicated by: David R. Larson
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 3845-3849
- MSC (2000): Primary 46L05
- DOI: https://doi.org/10.1090/S0002-9939-03-06991-0
- MathSciNet review: 1999933