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arXiv · 2502.13625

Automatic time continuity of positive matrix and operator semigroups

Jochen Glück
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Abstract

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.

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Jochen Glück. 2025-02-19. Automatic time continuity of positive matrix and operator semigroups. https://arxiv.org/abs/2502.13625

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