Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-27T07:01:22.866Z Has data issue: false hasContentIssue false
  • English
  • Français

Semigroup Compactifications of Direct and Semidirect Products

Published online by Cambridge University Press:  20 November 2018

Paul Milnes
Paul Milnes*
Affiliation:
Department of Mathematics, The University of Western OntarioLondon, Ontario, CanadaN6A 5B7
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A classical result of I. Glicksberg and K. de Leeuw asserts that the almost periodic compactification of a direct product S × T of abelian semigroups with identity is (canonically isomorphic to) the direct product of the almost periodic compactiflcations of S and T. Some efforts have been made to generalize this result and recently H. D. Junghenn and B. T. Lerner have proved a theorem giving necessary and sufficient conditions for an F-compactification of a semidirect product S⊗σT to be a semidirect product of compactiflcations of S and T. A different such theorem is presented here along with a number of corollaries and examples which illustrate its scope and limitations. Some behaviour that can occur for semidirect products, but not for direct products, is exposed

Keywords

22A1522A2043A60semitopological semigroup(semidirect) product(right topological) compactification
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 26 , Issue 2 , 01 June 1983 , pp. 233 - 240
Copyright
Copyright © Canadian Mathematical Society 1983

References

1. Berglund, J. F., Junghenn, H. D. and Milnes, P., Compact right topological semigroups and generalizations of almost periodicity, Lecture Notes in Mathematics, Vol. 663, Springer-Verlag, Berlin, 1978.Google Scholar
2. Berglund, J. F. and Milnes, P., Algebras of functions on semitopological left-groups, Trans. Amer. Math. Soc. 222 (1976), 157–178.Google Scholar
3. Chou, C., Weakly almost periodic functions and Fourier-Stieltjes algebras of locally compact groups.Google Scholar
4. de Leeuw, K. and Glicksberg, I., Almost periodic functions on semigroups, Acta Meth. 105 (1961), 99–140.Google Scholar
5. Ellis, R., Locally compact transformation groups, Duke Math. J. 24 (1957), 119–125.Google Scholar
6. Junghenn, H. D., C*-algebras of functions on direct products of semigroups, Rocky Mountain J. Math. 10 (1980), 589–597.Google Scholar
7. Junghenn, H. D., Distal compactifications of semigroups.Google Scholar
8. Junghenn, H. D. and Lerner, B. T., Semigroup compactifications of semidirect products, Trans. Amer. Math. Soc. 265 (1981), 393–404.Google Scholar
9. Milnes, P., Continuity properties of compact right topological groups, Proc. Camb. Phil. Soc. 86 (1979), 427–435.Google Scholar
10. Milnes, P., Almost periodic compactifications of direct and semidirect products Coll. Math. 44 (1981) 125–136.Google Scholar
11. Veech, W. A., Weakly almost periodic functions on semisimple Lie groups, Mona. Math. 88 (1979), 55–68.Google Scholar