Christensen-Evans theorem and extensions of GNS-symmetric quantum Markov semigroups

• URL: http://arxiv.org/abs/2203.00341v1
• Date: Tue, 1 Mar 2022 10:34:24 GMT
• Title: Christensen-Evans theorem and extensions of GNS-symmetric quantum Markov semigroups
• Authors: Melchior Wirth
• Abstract summary: We show the existence of GNS-symmetric extensions of GNS-symmetric quantum Markov semigroups. This implies that the generators of GNS-symmetric quantum Markov semigroups on finite-dimensional von Neumann algebra can be written in the form specified by Alicki's theorem.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this note we prove a refined version of the Christensen-Evans theorem for generators of uniformly continuous GNS-symmetric quantum Markov semigroups. We use this result to show the existence of GNS-symmetric extensions of GNS-symmetric quantum Markov semigroups. In particular, this implies that the generators of GNS-symmetric quantum Markov semigroups on finite-dimensional von Neumann algebra can be written in the form specified by Alicki's theorem.

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