Non-commutative metric topology on matrix state space
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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.References
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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
- 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
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 443-453
- MSC (2000): Primary 46L87, 58B30, 46L30
- DOI: https://doi.org/10.1090/S0002-9939-05-08036-6
- MathSciNet review: 2176013