Abstract
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 language | English |
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Pages (from-to) | 339-361 |
Number of pages | 23 |
Journal | Journal of Operator Theory |
Volume | 54 |
Issue number | 2 |
Publication status | Published - 2003 |