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Non-commutative metric topology on matrix state space

Wei Wu
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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.

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Wei Wu. 2004-10-27. Non-commutative metric topology on matrix state space. https://arxiv.org/abs/math/0410587

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