A REMARK ON INVARIANCE OF QUANTUM MARKOV SEMIGROUPS

Title & Authors
A REMARK ON INVARIANCE OF QUANTUM MARKOV SEMIGROUPS
Choi, Ve-Ni; Ko, Chul-Ki;

Abstract
In [3, 9], using the theory of noncommutative Dirichlet forms in the sense of Cipriani [6] and the symmetric embedding map, authors constructed the KMS-symmetric Markovian semigroup $\small{\{S_t\}_{t{\geq}0}}$ on a von Neumann algebra $\small{\cal{M}}$ with an admissible function f and an operator $\small{x\;{\in}\;{\cal{M}}}$. We give a sufficient and necessary condition for x so that the semigroup $\small{\{S_t\}_{t{\geq}0}}$ acts separately on diagonal and off-diagonal operators with respect to a basis and study some results.
Keywords
quantum Markov semigroups;diagonal operators;invariant subspaces;
Language
English
Cited by
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