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.File in questo prodotto:
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On the range of the generator of a quantum Markov semigroup_11311-976714_Fagnola.pdf
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