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))⊂XRTX 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 l(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.