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arXiv · 2204.13964

Analyticity of positive semigroups is inherited under domination

Jochen Glück
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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.

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Jochen Glück. 2022-04-29. Analyticity of positive semigroups is inherited under domination. https://arxiv.org/abs/2204.13964

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