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arXiv · 2412.17097

On the extension of one-parameter operator semigroups to completions of Archimedean vector lattices

Eduard Emelyanov
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Abstract

Extensions of one-parameter operator semigroups on Archimedean vector lattices to their order/ru-completions are studied. Existence and uniqueness of the extension to the ru-completion is established in the class of positive semigroups. An extension theorem for positive ru-continuos semigroups on vector lattices with property (R) is proved. This theorem allows one to abandon the requirement of ru-completeness in various results concerning positive ru-continuous semigroups.

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Eduard Emelyanov. 2024-12-22. On the extension of one-parameter operator semigroups to completions of Archimedean vector lattices. https://arxiv.org/abs/2412.17097

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