This article is cited in 3 papers

Embedding of a Uniquely Divisible Abelian Semigroup In a Convex Cone

I. V. Orlov

Crimea Federal University, Simferopol

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.

Keywords: Abelian semigroup, unique divisibility, convex cone, infinitesimal generator of an operator semigroup.

UDC: 512.53+517.98

Received: 29.07.2016
Revised: 15.03.2017

DOI: 10.4213/mzm11329

 English version: Mathematical Notes, 2017, 102:3, 361–368

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