We show that the commutant of the range of the infinitesimal generator of a norm-continuous quantum Markov semigroup on B(h), not consisting of identity maps, with a faithful normal invariant state is trivial whenever the fixed point algebra is atomic. As a consequence, two formulations of the irreversible (H, β)-KMS condition proposed in Ref. 2 are equivalent for this class of quantum Markov semigroups.

On the range of the generator of a quantum Markov semigroup

FAGNOLA, FRANCO
2015-01-01

Abstract

We show that the commutant of the range of the infinitesimal generator of a norm-continuous quantum Markov semigroup on B(h), not consisting of identity maps, with a faithful normal invariant state is trivial whenever the fixed point algebra is atomic. As a consequence, two formulations of the irreversible (H, β)-KMS condition proposed in Ref. 2 are equivalent for this class of quantum Markov semigroups.
2015
commutant; generator range; Quantum Markov semigroup; Applied Mathematics; Statistics and Probability; Mathematical Physics; Statistical and Nonlinear Physics
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/976714
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