  We establish adiabatic theorems with and without spectral gap condition for
general -- typically dissipative -- linear operators $A(t): D(A(t)) \subset X
\to X$ with time-dependent domains $D(A(t))$ in some Banach space $X$. In these
theorems, we do not require the considered spectral values $\lambda(t)$ of
$A(t)$ to be (weakly) semisimple. We then apply our general theorems to the
special case of skew-adjoint operators $A(t) = 1/i A_{a(t)}$ defined by
symmetric sesquilinear forms $a(t)$ and thus generalize, in a very simple way,
the only adiabatic theorem for operators with time-dependent domains known so
far.
