A Remark on the structure of symmetric quantum dynamical semigroups on von Neumann algebras

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We study the structure of the generator of a symmetric, conservative quantum dynamical semigroup with norm-bounded generator on a von Neumann algebra equipped with a faithful semifinite trace. For von Neumann algebras with abelian commutant (i.e. type I von Neumann algebras), we give a necessary and sufficient algebraic condition for the generator of such a semigroup to be written as a sum of square of self-adjoint derivations of the von Neumann algebra. This generalizes some of the results obtained by Albeverio, H(phi)egh-Krohn and Olsen [Alb] for the special case of the finite dimensional matrix algebras. We also study similar questions for a class of quantum dynamical semigroups with unbounded generators.
accepted in Infinite Dimensional Analysis, Quantum Probability and Related Toplics (World Scientific)

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Mathematical Physics, Functional Analysis

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http://salesiana.dossiersoluciones.com/handle/123456789/57116

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math-ph/0207047
 http://arxiv.org/abs/math-ph/0207047

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arXiv