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

 

Non-commutative metric topology on matrix state space


Author: Wei Wu
Journal: Proc. Amer. Math. Soc. 134 (2006), 443-453
MSC (2000): Primary 46L87, 58B30, 46L30
Published electronically: June 29, 2005
MathSciNet review: 2176013
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Abstract | References | Similar Articles | Additional Information

Abstract: We present an operator space version of Rieffel's theorem on the agreement of the metric topology, on a subset of the Banach space dual of a normed space, from a seminorm with the weak*-topology. As an application we obtain a necessary and sufficient condition for the matrix metric from an unbounded Fredholm module to give the BW-topology on the matrix state space of the $C^*$-algebra. Motivated by recent results we formulate a non-commutative Lipschitz seminorm on a matrix order unit space and characterize those matrix Lipschitz seminorms whose matrix metric topology coincides with the BW-topology on the matrix state space.


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Additional Information

Wei Wu
Affiliation: Department of Mathematics, East China Normal University, Shanghai 200062, People’s Republic of China
Email: wwu@math.ecnu.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08036-6
PII: S 0002-9939(05)08036-6
Keywords: BW-topology, generalized Dirac operator, matrix Lipschitz seminorm, matrix seminorm, matrix state space, operator space
Received by editor(s): June 6, 2003
Received by editor(s) in revised form: September 20, 2004
Published electronically: June 29, 2005
Communicated by: David R. Larson
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.