University of Oulu

M. Filali, J. Galindo, Algebraic structure of semigroup compactifications: Pym's and Veech's Theorems and strongly prime points, Journal of Mathematical Analysis and Applications, Volume 456, Issue 1, 2017, Pages 117-150, ISSN 0022-247X,

Algebraic structure of semigroup compactifications : Pym’s and Veech’s Theorems and strongly prime points

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Author: Filali, M.1; Galindo, J.2
Organizations: 1Department of Mathematical Sciences, University of Oulu, Oulu, Finland
2Instituto Universitario de Matemáticas y Aplicaciones (IMAC), Universidad Jaume I, E-12071, Castellón, Spain
Format: article
Version: accepted version
Access: embargoed
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Language: English
Published: Elsevier, 2017
Publish Date: 2019-07-04


The spectrum of an admissible subalgebra \(\mathscr{A}(G)\) of \(LUC(G)(G)\), the algebra of right uniformly continuous functions on a locally compact group \(G\), constitutes a semigroup compactification \(G^{\mathscr{A}}\) of \(G\). In this paper we analyze the algebraic behaviour of those points of \(G^{\mathscr{A}}\) that lie in the closure of \(\mathscr{A}(G)\)-sets, sets whose characteristic function can be approximated by functions in \(\mathscr{A}(G)\). This analysis provides a common ground for far reaching generalizations of Veech’s property (the action of \(G\) on \(G^{LUC(G)}\) is free) and Pym’s Local Structure Theorem. This approach is linked to the concept of translation-compact set, recently developed by the authors, and leads to characterizations of strongly prime points in \(G^{\mathscr{A}}\), points that do not belong to the closure of \(G^⁎G^⁎\), where \(G^⁎ = G^{\mathscr{A}}\setminus G\). All these results will be applied to show that, in many of the most important algebras, left invariant means of \(\mathscr{A}(G)\) (when such means are present) are supported in the closure of \(G^⁎G^⁎\).

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Series: Journal of mathematical analysis and applications
ISSN: 0022-247X
ISSN-E: 1096-0813
ISSN-L: 0022-247X
Volume: 456
Issue: 1
Pages: 117 - 150
DOI: 10.1016/j.jmaa.2017.06.038
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Funding: The work was partially supported by the program Short-Term International Research Visits, University of Oulu (grant 2402070).
Copyright information: © 2017. This manuscript version is made available under the CC-BY-NC-ND 4.0 license