Remarks on the Structure of Dirichlet Forms on Standard Forms of von Neumann Algebras

Details Remarks on the Structure of Dirichlet Forms on Standard Forms of von Neumann Algebras Remarks on the Structure of Dirichlet Forms on Standard Forms of von Neumann Algebras

2004-01-03

arxiv.org/abs/math-ph/0401001v1

Physics

Mathematical Physics

Scientific paper

For a von Neumann algebra M acting on a Hilbert space H with a cyclic and separating vector v, we investigate the structure of Dirichlet forms on the natural standard form associated with the pair (M,v). For a general Lindblad type generator L of a conservative quantum dynamical semigroup on M, we give sufficient conditions so that the operator S induced by L via the symmetric embedding of M into H to be self-adjoint. It turns out that the self-adjoint operator S can be written in the form of a Dirichlet operator associated to a Dirichlet form given in [23]. In order to make the connection possible, we also extend the range of applications of the formula in [23].

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