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

Research output: Contribution to journalArticle

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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 languageEnglish
Article number113504
JournalJournal of Mathematical Physics
Volume48
Issue number11
DOIs
Publication statusPublished - 2007 Dec 10

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Dirichlet Form
Scientific notation
Von Neumann Algebra
algebra
generators
derivation
Generator
Completely Continuous
decomposition
Decompose
Separable Hilbert Space
Hilbert space
embedding
Divergence
divergence
Semigroup
operators
Operator
Form

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.

In: Journal of Mathematical Physics, Vol. 48, No. 11, 113504, 10.12.2007.

Research output: Contribution to journalArticle

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