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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On characterizations of commutativity of C$^*$-algebras


Authors: Guoxing Ji and Jun Tomiyama
Journal: Proc. Amer. Math. Soc. 131 (2003), 3845-3849
MSC (2000): Primary 46L05
Published electronically: March 25, 2003
MathSciNet review: 1999933
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-03-06991-0
PII: S 0002-9939(03)06991-0
Keywords: C$^*$-algebra, commutativity
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
Article copyright: © Copyright 2003 American Mathematical Society