Speaker: Valentin A. ZAGREBNOV，Institut de Mathematiques de Marseille

Title: About product formulae for non-autonomous Gibbs semigroups

Language: Chinese

Time & Venue: 2024.06.21 10:30-11:30 南楼N820

Abstract: We study a linear evolution equation corresponding to small non-autonomous Holder continuous perturbations of the Gibbs semigroup on a separable Hilbert space. It is shown that strongly continuous evolution family {U(t,s)}0≤s≤t≤T which solves the non- autonomous Cauchy problem can be constructed for s < t as a limit in the trace-norm topology of the product approximants {Un (t,s)}{0≤s<t≤T} , n ≥ 1. We prove that estimates of the rate of convergence of these approximants to the trace-class solution operator {U(t,s)}{0≤s<t≤T} are related to estimates established for their rates of convergence in the operator-norm topology.This result is partially based on the recent book: Trotter-Kato Product Formulæ (Birkhauser-Springer 2024) by Valentin A.Zagrebnov, Hagen Neidhardt and Takashi Ichinose.