Non-commutative Metric Topology on Matrix State Space
نویسنده
چکیده
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 noncommutative 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.
منابع مشابه
Non-commutative Metrics on Matrix State Spaces
We use the theory of quantization to introduce non-commutative versions of metric on state space and Lipschitz seminorm. We show that a lower semicontinuous matrix Lipschitz seminorm is determined by their matrix metrics on the matrix state spaces. A matrix metric comes from a lower semicontinuous matrix Lip-norm if and only if it is convex, midpoint balanced, and midpoint concave. The operator...
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