Remarks on the Structure of Dirichlet Forms on Standard Forms of von Neumann Algebras
Mathematical Physics
2007-05-23 v1 Dynamical Systems
math.MP
Abstract
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].
Keywords
Cite
@article{arxiv.math-ph/0401001,
title = {Remarks on the Structure of Dirichlet Forms on Standard Forms of von Neumann Algebras},
author = {Y. M. Park},
journal= {arXiv preprint arXiv:math-ph/0401001},
year = {2007}
}