Analyticity of positive semigroups is inherited under domination
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2022
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910835067060224 |
|---|---|
| author | Glück, Jochen |
| author_facet | Glück, Jochen |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_13964 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Analyticity of positive semigroups is inherited under domination Glück, Jochen Functional Analysis 47D06, 47B65, 47A10 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. |
| title | Analyticity of positive semigroups is inherited under domination |
| topic | Functional Analysis 47D06, 47B65, 47A10 |
| url | https://arxiv.org/abs/2204.13964 |