Solution Operator for Non-Autonomous Perturbation of Gibbs Semigroup

The paper is devoted to a linear dynamics for non-autonomous perturbation of the Gibbs semigroup on a separable Hilbert space. It is shown that evolution family {U(t, s)} 0≤s≤t solving the non-autonomous Cauchy problem can be approximated in the trace-norm topology by product formulae. The rate of convergence of product formulae approximants {U n (t, s)} {0≤s≤t,n≥1} to the solution operator {U(t, s)} {0≤s≤t} is also established