### Abstract

For a bounded generator G of a weakly* -continuous, completely positive, KMS-symmetric Markovian semigroup on a von Neumann algebra M acting on a separable Hilbert space H, let H be the operator induced by G via the symmetric embedding of M into H. We decompose the Dirichlet form associated with H into a direct integral of forms whose associated generators are divergences of derivations. Moreover, if the derivations are inner, then the Dirichlet form can be written as the form given by Park [Infinite Dimen. Anal. Quantum Probab., Relat. Top. 3, 1 (2000); 8, 179 (2005)].

Original language | English |
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Article number | 113504 |

Journal | Journal of Mathematical Physics |

Volume | 48 |

Issue number | 11 |

DOIs | |

Publication status | Published - 2007 Dec 10 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

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**Remarks on the decomposition of Dirichlet forms on standard forms of von Neumann algebras.** / Ko, Chul Ki.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Remarks on the decomposition of Dirichlet forms on standard forms of von Neumann algebras

AU - Ko, Chul Ki

PY - 2007/12/10

Y1 - 2007/12/10

N2 - For a bounded generator G of a weakly* -continuous, completely positive, KMS-symmetric Markovian semigroup on a von Neumann algebra M acting on a separable Hilbert space H, let H be the operator induced by G via the symmetric embedding of M into H. We decompose the Dirichlet form associated with H into a direct integral of forms whose associated generators are divergences of derivations. Moreover, if the derivations are inner, then the Dirichlet form can be written as the form given by Park [Infinite Dimen. Anal. Quantum Probab., Relat. Top. 3, 1 (2000); 8, 179 (2005)].

AB - For a bounded generator G of a weakly* -continuous, completely positive, KMS-symmetric Markovian semigroup on a von Neumann algebra M acting on a separable Hilbert space H, let H be the operator induced by G via the symmetric embedding of M into H. We decompose the Dirichlet form associated with H into a direct integral of forms whose associated generators are divergences of derivations. Moreover, if the derivations are inner, then the Dirichlet form can be written as the form given by Park [Infinite Dimen. Anal. Quantum Probab., Relat. Top. 3, 1 (2000); 8, 179 (2005)].

UR - http://www.scopus.com/inward/record.url?scp=36749085231&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36749085231&partnerID=8YFLogxK

U2 - 10.1063/1.2804751

DO - 10.1063/1.2804751

M3 - Article

AN - SCOPUS:36749085231

VL - 48

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 11

M1 - 113504

ER -