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We also prove a related abstract result: if $(T(t))_{t \in [0,\infty)}$ is a positive $C_0$-semigroup on a Banach lattice $X$ with order continuous norm, then the span of the cone $X_{-1,+}$ in the extrapolation space $X_{-1}$ is a vector lattice. This complements results obtained by Bátkai, Jacob, Wintermayr, and Voigt in the context of perturbation theory and provides additional context for the theory of infinite-dimensional positive systems.
From: Sahiba Arora [view email]
[v1]
Tue, 2 Apr 2024 17:20:12 UTC (33 KB)
[v2]
Fri, 16 Aug 2024 14:23:29 UTC (40 KB)
[v3]
Tue, 4 Mar 2025 02:45:36 UTC (42 KB)
[v4]
Wed, 17 Jun 2026 20:31:04 UTC (42 KB)
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