Automatic time continuity of positive matrix and operator semigroups
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910835651117056 |
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| author | Glück, Jochen |
| author_facet | Glück, Jochen |
| contents | We consider a matrix semigroup $T: [0,\infty) \to \mathbb{R}^{d \times d}$ without assuming any measurability properties and show that, if $T$ is bounded close to $0$ and $T(t) \ge 0$ entrywise for all $t$, then $T$ is continuous. This complements classical results for the scalar-valued case. We also prove an analogous result if $T$ takes values in the positive operators over a sequence space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_13625 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Automatic time continuity of positive matrix and operator semigroups Glück, Jochen Functional Analysis Dynamical Systems 47D06, 47B65 We consider a matrix semigroup $T: [0,\infty) \to \mathbb{R}^{d \times d}$ without assuming any measurability properties and show that, if $T$ is bounded close to $0$ and $T(t) \ge 0$ entrywise for all $t$, then $T$ is continuous. This complements classical results for the scalar-valued case. We also prove an analogous result if $T$ takes values in the positive operators over a sequence space. |
| title | Automatic time continuity of positive matrix and operator semigroups |
| topic | Functional Analysis Dynamical Systems 47D06, 47B65 |
| url | https://arxiv.org/abs/2502.13625 |