Extension of additive functionals and semicharacters on commutative semigroups

descriptionPublicationkeyboard_double_arrow_right Article 01 Dec 1979 Germany English Publisher:Springer Science and Business Media LLCJournal:Semigroup Forum, volume 18, pages 293-305 (issn: 0037-1912, eissn: 1432-2137,

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Authors: Kranz, P.;

doi: 10.1007/bf02574194

Extension of additive functionals and semicharacters on commutative semigroups

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Abstract

Let S be a commutative semigroup and So a subsemigroup. The present paper establishes a necessary and sufficient condition in order that any real additive functional ϕ0 defined on So and dominated there by a real subadditive functional p defined on S, admit an additive extension to S such that ϕ≤p. This result is a strengthening of a result of R.Kaufman [3]. From this easily follow recent results of Kobayashi [5] and Putcha, Tamura [9] on extension of semigroup homomorphisms. Also a result of Ross on extension of semicharacters can be deduced from this result.

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Germany

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Keywords

510.mathematics, extension of additive functionals, Representation of semigroups; actions of semigroups on sets, subadditive functional, Mappings of semigroups, Functional equations for functions with more general domains and/or ranges, semicharacter, Article

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