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Journal of Operator Theory

Volume 75, Issue 2, Spring 2016  pp. 443-474.

New approaches to honesty theory and applications in quantum dynamical semigroups

Authors:  Chin Pin Wong
Author institution: Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, U.K.

Summary: We prove some new characterisations of honesty of the perturbed semigroup in Kato's perturbation theorem on abstract state spaces via three approaches, namely using the mean ergodicity of operators, adjoint operators and the uniqueness of the perturbed semigroup. We then apply Kato's theorem on abstract state spaces and the honesty theory linked to it to the study of quantum dynamical semigroups. We show that honesty is the natural generalisation of the notion of conservativity.

Keywords: substochastic semigroups, quantum dynamical semigroups, honesty, conservativity

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