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A remark on ergodicity of quantum Markovian semigroups
대한수학회 (The Korean Mathematical Society)|2009.01|대한수학회논문집 (Communications of the KMS)|제24권 제1호|pp. 99-109
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The aim of this paper is to find the set of the fixed elements and the set of elements for which equality holds in Schwarz inequality for the KMS-symmetric Markovian semigroup {S_t}_{t≥0} given in [10]. As an application, we study some properties such as the ergodicity and the asymptotic behavior of the semigroup.
Abstract
The aim of this paper is to find the set of the fixed elements and the set of elements for which equality holds in Schwarz inequality for the KMS-symmetric Markovian semigroup {S_t}_{t≥0} given in [10]. As an application, we study some properties such as the ergodicity and the asymptotic behavior of the semigroup.
참고문헌 (12)
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- Y. M. Park, "Remarks on the structure of Dirichlet forms on standard forms of von Neumann algebras", Inf. Dim. Anal. Quantum Probab. Related Topics, 8, pp.179~197 (2005)
- Y. M. Park, "Ergodic property of Markovian semigroups on standard forms of von Neumann algebras", J. Math. Phys., 46, pp.113507-1~113507-13 (2005)
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