Product approximations of solution operators for non‐autonomous perturbations of Gibbs semigroups
Valentin Anatol'evich Zagrebnov · Mathematische Nachrichten · 2022
Abstract The paper is devoted to study of linear evolution equation corresponding to a small non‐autonomous Hölder continuous perturbations of Gibbs semigroups on a separable Hilbert space. It is shown that an evolution family solving the non‐autonomous Cauchy problem can be constructed for as a limit in the trace‐norm topology of the product trace‐class approximants , . We also proved that estimates of the rate of convergence of these approximants to the trace‐norm continuous solution operator are related to estimates established for their rates of convergence in the operator‐norm topology.