Adiabatic theorems for general linear operators with time-independent domains.

We establish adiabatic theorems with and without spectral gap conditions for general — typically dissipative — linear operators A (t) : D (A (t)) ⊂ X → X with time-independent domains D (A (t)) = D in some Banach space X. Compared to the previously known adiabatic theorems — especially those without a spectral gap condition — we do not require the considered spectral values λ (t) of A (t) 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. [ABSTRACT FROM AUTHOR]