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An Index Theory For
Quantum Dynamical Semigroups

Author: B. V. Rajarama Bhat
Journal: Trans. Amer. Math. Soc. 348 (1996), 561-583
MSC (1991): Primary 46L57, 81S25, 46L55
MathSciNet review: 1329528
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Abstract: W. Arveson showed a way of associating continuous tensor product systems of Hilbert spaces with endomorphism semigroups of type I factors. We do the same for general quantum dynamical semigroups through a dilation procedure. The product system so obtained is the index and its dimension is a numerical invariant for the original semigroup.

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Additional Information

B. V. Rajarama Bhat
Affiliation: The Fields Institute, 222 College Street, Toronto, Ontario, Canada
Email: E-mail address:

Keywords: Completely positive maps, semigroups, Markov dilations, continuous tensor products
Received by editor(s): May 27, 1994
Additional Notes: This research was supported by a fellowship from INDAM (ITALY)
Article copyright: © Copyright 1996 American Mathematical Society

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