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BURES DISTANCE FOR COMPLETELY POSITIVE MAPS
https://doi.org/10.1142/S0219025713500318Cited by:2 (Source: Crossref)
Abstract
Bures had defined a metric on the set of normal states on a von Neumann algebra using GNS representations of states. This notion has been extended to completely positive maps between C*-algebras by Kretschmann, Schlingemann and Werner. We present a Hilbert C*-module version of this theory. We show that we do get a metric when the completely positive maps under consideration map to a von Neumann algebra. Further, we include several examples and counter examples. We also prove a rigidity theorem, showing that representation modules of completely positive maps which are close to the identity map contain a copy of the original algebra.
AMSC: 46L08, 46L30
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