Adiabatic theorems for general linear operators with time-independent domains

Abstract

We establish adiabatic theorems with and without spectral gap conditions for general — typically dissipative — linear operators [Formula: see text] with time-independent domains [Formula: see text] in some Banach space [Formula: see text]. Compared to the previously known adiabatic theorems — especially those without a spectral gap condition — we do not require the considered spectral values [Formula: see text] of [Formula: see text] to be (weakly) semisimple. We also impose only fairly weak regularity conditions. Applications are given to slowly time-varying open quantum systems and to adiabatic switching processes.