Feynman-Kac perturbation of \(C^*\) quantum stochastic flows (Q6623997)

The authors extend the method of Feynman-Kac perturbation of quantum stochastic processes, usually developed within the framework of processes on von Neumann algebras, to \(C^*\) quantum stochastic flows. In this framework much greater care is needed. The theory of operator spaces is exploited to enable a broadening of the scope to flows on \(C^*\) algebras. The hypotheses that need to be verified in this general setting may seem numerous, but the authors provide auxiliary results that allow simplification in many of the cases which arise in practice. The last section of this very well written paper provides a wide variety of illustrative examples, which is very useful to realize both the difficulty of the mathematical problems and the possible applications of the results.