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 A remark on invariance of quantum Markov semigroups Commun. Korean Math. Soc. 2008 Vol. 23, No. 1, 81-93 Printed March 1, 2008 Veni Choi and Chul Ki Ko Ajou University and Yonsei University Abstract : In \cite{BKP,Pa}, using the theory of noncommutative Dirichlet forms in the sense of Cipriani \cite{Cip} and the symmetric embedding map, authors constructed the KMS-symmetric Markovian semigroup $\{S_t\}_{t\ge0}$ on a von Neumann algebra $\cM$ with an admissible function $f$ and an operator $x\in\cM$. We give a sufficient and necessary condition for $x$ so that the semigroup $\{S_t\}_{t\ge0}$ 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 MSC numbers : 46L55, 37A60 Downloads: Full-text PDF