Analyticity of positive semigroups is inherited under domination

Abstract

For positive $C_0$-semigroups $S$ and $T$ on a Banach lattice such that $S(t)\le T(t)$ for all times $t$, we prove that analyticity of $T$ implies analyticity of $S$. 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 $S$ and $T$ on a vector-valued function space.

arXiv comment5 pages. This is version 2; Examples 7 and 8 were added compared to version 1