Automatic time continuity of positive matrix and operator semigroups

2025/02/19 by Jochen Glück, Glück, Jochen
Computer Science · #47B65 #47D06 #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2502.13625

openalex publication_date 2025/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We consider a matrix semigroup T: [0,∞) → ℝ^{d × d} without assuming any measurability properties and show that, if T is bounded close to 0 and T(t) ≥ 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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