Abstract
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.
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Acknowledgements
We would like to express our gratitude to Marko Kandić for insightful comments and meticulous proofreading which improved the manuscript. The first author would also like to thank Marko for professional guidance. Special thanks belongs to Jochen Glück for his valuable remarks.
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The authors acknowledge financial support from the Slovenian Research Agency, Grant No. P1-0222.
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Kaplin, M., Fijavž, M.K. Generation of relatively uniformly continuous semigroups on vector lattices. Anal Math 46, 293–322 (2020). https://doi.org/10.1007/s10476-020-0025-y
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DOI: https://doi.org/10.1007/s10476-020-0025-y