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http://dx.doi.org/10.4134/CKMS.2008.23.1.081

A REMARK ON INVARIANCE OF QUANTUM MARKOV SEMIGROUPS  

Choi, Ve-Ni (DIVISION OF GENERAL STUDIES AJOU UNIVERSITY)
Ko, Chul-Ki (UNIVERSITY COLLEGE YONSEI UNIVERSITY)
Publication Information
Communications of the Korean Mathematical Society / v.23, no.1, 2008 , pp. 81-93 More about this Journal
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;
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1 L. Accardi, F. Fagnola, and S. Hachicha, Generic q-Markov semigroups and speed of convergence of q-algorithms, Inf. Dim. Anal. Quantum Probab. Related Topics 9 (2006), 567-594   DOI   ScienceOn
2 C. Bahn, C. K. Ko, and Y. M. Park, Dirichlet forms and symmetric Markovian semigroups on CCR algebras with quasi-free states, J. Math. Phys. 44 (2003), 723-753   DOI   ScienceOn
3 O. Bratteli and D. W. Robinson, Operator algebras and quantum statistical mechanics, Springer-Verlag, New York-Heidelberg-Berlin, vol I (1979), vol. II (1981)
4 Y. M. Park, Construction of Dirichlet forms on standard forms of von Neumann algebras, Inf. Dim. Anal. Quantum Probab. Related Topics 3 (2000), 1-14   DOI   ScienceOn
5 K. R. Parthasarathy, An Introduction to Quantum Stochastic Calculus, Birkhauser, Basel, 1992
6 V. S. Sunder, An Invitation to von Neumann Algebras, Springer-Verlag, Newyork Berlin Heidelberg London Paris Tokyo, 1986
7 F. Cipriani, F. Fagnola, and J. M. Lindsay, Spectral Analysis and Feller Properties for Quantum Ornstein-Uhlenbeck Semigroups, Comm. Math. Phys. 210 (2000), 85-105   DOI
8 F. Fagnola and R. Quezada, Two-photon and emission process, Inf. Dim. Anal. Quantum Probab. Related Topics 8 (2005), 573-591   DOI   ScienceOn
9 R. Carbone, F. Fagnola, and S. Hachicha, Generic quantum Markov semigroups: the Gaussian gauge invariant case, priprint
10 F. Cipriani, Dirichlet forms and Markovian semigroups on standard forms of von Neumann algebras, J. Funct. Anal. 147 (1997), 259-300   DOI   ScienceOn
11 S. Albeverio and R. Hoegh-Krohn, Dirichlet forms and Markovian semigroups on C* - algebras, Comm. Math. Phys. 56 (1977), 173-187   DOI