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A REMARK ON INVARIANCE OF QUANTUM MARKOV SEMIGROUPS

Choi, Ve-Ni;Ko, Chul-Ki

  • Published : 2008.01.31

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 $\{S_t\}_{t{\geq}0}$ on a von Neumann algebra $\cal{M}$ with an admissible function f and an operator $x\;{\in}\;{\cal{M}}$. We give a sufficient and necessary condition for x so that the semigroup $\{S_t\}_{t{\geq}0}$ 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

References

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