Extension of characters on *-semigroups
type: Item
instance of: scholarly article
title: Extension of characters on *-semigroups
zbMATH Open document ID: 0629.20040
DOI: 10.1007/BF01456974
author: Torben Maack Bisgaard
published in: Mathematische Annalen
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164460
review text: A character on an abelian semigroup S with an involution \((x\to x^ *)\) is, by definition, a nonzero homomorphism \(\rho\) : \(S\to {\mathbb{C}}\) satisfying \(\rho (x^ *)=\overline{\rho (x)}\). Necessary and sufficient conditions are given for a fixed character, or every character, on a given *-subsemigroup T of S to be extendible to a character on S. These conditions are similar to those discovered by \textit{K. A. Ross} [Proc. Am. Math. Soc. 10, 579-583 (1959; Zbl 0090.017)] and by \textit{P. Hill} [J. Algebra 5, 16-24 (1967; Zbl 0146.031)] in the case of complex homomorphisms on abelian semigroups without involution. It is shown that any countable (resp. infinite) *-subsemigroup \(T_ 0\) of S is contained in a *-subsemigroup T of S which is countable (resp. equipotent to \(T_ 0)\) and such that every character on T extends to a character on S.
Mathematics Subject Classification ID: 20M30
zbMATH DE Number: 4023583
zbMATH Keywords: character
zbMATH Keywords: abelian semigroup
zbMATH Keywords: involution
zbMATH Keywords: extendible
MaRDI profile type: Publication
cites work: Unique disintegration of arbitrary positive definite functions on \(*\)- divisible semigroups
cites work: Characters of commutative semigroups
cites work: Some theorems concerning the dual of a commutative semigroup
cites work: A Note on Extending Semicharacters on Semigroups
cites work: Characters on inverse semigroups
OpenAlex ID: W2002022660
description: scientific article; zbMATH DE number 4023583