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

Research output: Contribution to journalArticle

2 Citations (Scopus)

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

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Fingerprint Dive into the research topics of 'Remarks on the decomposition of Dirichlet forms on standard forms of von Neumann algebras'. Together they form a unique fingerprint.

  • Cite this