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Embedding of a uniquely divisible Abelian semigroup in a convex cone

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Abstract

It is proved that every uniquely divisible Abelian semigroup admits an injective subadditive embedding in a convex cone. As an application, the classical theory of generators of one-parameter operator semigroups is generalized to the case in which the parameter ranges over a uniquely divisible semigroup.

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Authors and Affiliations

  1. “Mathematical Notes,” Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia

    I. V. Orlov

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  1. I. V. Orlov
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Correspondence to I. V. Orlov.

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Original Russian Text © I. V. Orlov, 2017, published in Matematicheskie Zametki, 2017, Vol. 102, No. 3, pp. 396–404.

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Orlov, I.V. Embedding of a uniquely divisible Abelian semigroup in a convex cone. Math Notes 102, 361–368 (2017). https://doi.org/10.1134/S0001434617090061

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  • DOI: https://doi.org/10.1134/S0001434617090061

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