We prove a Hille–Yosida type theorem for relatively uniformly continuous positive semigroups on vector lattices. We introduce the notions of relatively uniformly continuous, differentiable, and integrable functions on ℝ + . These notions allow us to study the generators of relatively uniformly continuous semigroups. Our main result provides sufficient and necessary conditions for an operator to be the generator of an exponentially order bounded, relatively uniformly continuous, positive semigroup.

中文翻译：

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矢量格上相对一致连续半群的生成

我们证明了向量格上相对一致连续的正半群的 Hille-Yosida 型定理。我们在 ℝ + 上引入了相对一致连续、可微和可积函数的概念。这些概念使我们能够研究相对一致连续半群的生成元。我们的主要结果为算子成为指数阶有界、相对一致连续、正半群的生成器提供了充分必要的条件。