New Approaches to Honesty Theory and Applications in Quantum Dynamical Semigroups

Chin Pin Wong

New Approaches to Honesty Theory and Applications in Quantum Dynamical Semigroups

Functional Analysis 2015-07-27 v1

Authors: Chin Pin Wong

Abstract

We prove some new characterisations of honesty of the perturbed semigroup in Kato's Perturbation Theorem on abstract state spaces via three approaches, namely mean ergodicity of operators, adjoint operators and 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

honesty theory perturbed semigroup Kato perturbation theorem quantum dynamical semigroup mean ergodicity adjoint operator conservativity

Cite

@article{arxiv.1507.06880,
  title  = {New Approaches to Honesty Theory and Applications in Quantum Dynamical Semigroups},
  author = {Chin Pin Wong},
  journal= {arXiv preprint arXiv:1507.06880},
  year   = {2015}
}