Infinite Dimensional Analysis Quantum Probability and Related Topics

MINIMAL QUANTUM DYNAMICAL SEMIGROUP ON A VON NEUMANN ALGEBRA

Debashish Goswami, Kalyan B. Sinha

Published Jun 1, 1999• 2 citations

Abstract

Given a formal unbounded generator, the minimal quantum dynamical semigroup on a von Neumann algebra is constructed. A set of equivalent necessary and sufficient conditions for the conservativity of the minimal semigroup is given and in the case when it is not conservative, a distinguished family of conservative perturbations of the semigroup is studied. Finally, some of these results are applied to the classical Markov semigroup with arbitrary state space.

DOI: 10.1142/s0219025799000126

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