For positive
C
0
C_0
-semigroups
S
S
and
T
T
on a Banach lattice such that
S
(
t
)
≤
T
(
t
)
S(t) \le T(t)
for all times
t
t
, we prove that analyticity of
T
T
implies analyticity of
S
S
. This answers an open problem posed by Arendt in 2004.
Our proof is based on a spectral theoretic argument: we apply spectral theory of positive operators to multiplication operators that are induced by
S
S
and
T
T
on a vector-valued function space.