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Non-commutative metric topology on matrix state space
Author(s):
Wei
Wu
Journal:
Proc. Amer. Math. Soc.
134
(2006),
443-453.
MSC (2000):
Primary 46L87, 58B30, 46L30
Posted:
June 29, 2005
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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  -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:
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
Posted:
June 29, 2005
Communicated by:
David R. Larson
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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