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On characterizations of commutativity of C-algebras

Author(s): Guoxing Ji; Jun Tomiyama
Journal: Proc. Amer. Math. Soc. 131 (2003), 3845-3849.
MSC (2000): Primary 46L05
Posted: March 25, 2003
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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.

References:

1.: E. Effros and Z-J. Ruan, Operator Spaces, London Math.Soc. Monographs 23, 2000, Oxford Sci. Pub. MR 2002a:46082
2.: T. Ogasawara, A theorem on operator algebras, J. Sci. Hiroshima Univ. 18 (1955), 307-309. MR 17:514a
3.: G. K. Pedersen, C-algebras and their automorphism groups, 1979, Academic Press Inc. (London) MR 81e:46037
4.: M.Uchiyama,Commutativity of selfadjoint opearators, Pacific J. Math. 161 (1993), 385-392. MR 94f:47027
5.: M. Takesaki, Theory of operator algebras I, 1979, Springer-Verlag, New York, Inc. MR 81e:46038
6.: Wei Wu, An order characterization of commutativity for $C^{\ast}$ -algebras, Proc. Amer. Math. Soc., 129 (2001), 983-987. MR 2001j:46084

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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: 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
Posted: 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 of article: Copyright 2003, American Mathematical Society


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