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In [3, 9], using the theory of noncommutative Dirichlet formsin the sense of Cipriani [6] and the symmetric embedding map, authorsconstructed the KMS-symmetric Markovian semigroup {St}t≥0 on a vonNeumann algebra M with an admissible function f and an operator x∈M . We give a sucient and necessary condition for x so that the semigroup {St}t≥0 acts separately on diagonal and off-diagonal operatorswith respect to a basis and study some results.
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참고문헌 (11)
참고문헌 신청
. R. Parthasarathy / 1992 / An Introduction to Quantum Stochastic Calculus, Birkh¨auser / Basel
C. Bahn / 2003 / Dirichlet forms and symmetric Markovian semigroups on CCR algebras with quasi-free states / J. Math. Phys 44 : 723 ~ 753
F. Cipriani / 1997 / Dirichlet forms and Markovian semigroups on standard forms of von Neumann algebras / J. Funct. Anal 147 : 259 ~ 300
F. Cipriani / 2000 / Spectral Analysis and Feller Properties for Quantum Ornstein-Uhlenbeck Semigroups / Comm. Math. Phys 210 : 85 ~ 105
F. Fagnola / 2005 / Two-photon and emission process / Inf. Dim. Anal. Quantum Probab. Related Topics 8 : 573 ~ 591
C. Bahn / 2003 / Dirichlet forms and symmetric Markovian semigroups on CCR algebras with quasi-free states / J. Math. Phys 44 : 723 ~ 753
F. Cipriani / 1997 / Dirichlet forms and Markovian semigroups on standard forms of von Neumann algebras / J. Funct. Anal 147 : 259 ~ 300
F. Cipriani / 2000 / Spectral Analysis and Feller Properties for Quantum Ornstein-Uhlenbeck Semigroups / Comm. Math. Phys 210 : 85 ~ 105
F. Fagnola / 2005 / Two-photon and emission process / Inf. Dim. Anal. Quantum Probab. Related Topics 8 : 573 ~ 591
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