A probabilistic index for completely positive maps and an application

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The probabilistic index of a completely positive map is defined in analogy with a formula of M. Pimsner and S. Popa for conditional expectations. As an application, we describe a new strategy for computing the Jones index of the range of certain endomorphisms. We use extended transition operators to associate to an endomorphism a unital completely positive map acting on a finite dimensional matrix algebra. Then the index to be computed equals the probabilistic index of this map. For a class of examples we get a complete classification.
Original languageEnglish
Pages (from-to)339-361
Number of pages23
JournalJournal of Operator Theory
Issue number2
Publication statusPublished - 2003


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