Abstract
Let ℳ be a von Neumann algebra with a cyclic and separating vector Ω and let ω(·) denote the corresponding vector state, i.e., ω(A)=(Ω, AΩ) A ∈ ℳ. We have proved that a positive semigroup τ on ℳ can induce the dynamical semigroup in the GNS representation associated with ω if the state ω is a τ-invariant one. Some applications are given.
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Majewski, W.A. Remarks on positive semigroups. Lett Math Phys 6, 437–440 (1982). https://doi.org/10.1007/BF00405863
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DOI: https://doi.org/10.1007/BF00405863