Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-24T12:49:01.444Z Has data issue: false hasContentIssue false
  • English
  • Français

Characterization of finite amenable transformation semigroups

Published online by Cambridge University Press:  09 April 2009

Carroll Wilde
Carroll Wilde
Affiliation:
Naval Postgraduate School Monterey, California, 93940, U.S.A.
Rights & Permissions [Opens in a new window]

Extract

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.

Abstract. In this paper we develop necessary and sufficient conditions for a finite transformation semigroup to have a mean value which is invariant under the induced shift operators. The structure of such transformation semigroups is described and an explicit description of all possible invariant means given.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 15 , Issue 1 , February 1973 , pp. 86 - 93
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Granirer, E. E.. ‘On amenable groups with a finite-dimensional set of invariant means I’, Ill. J. Math. 7 (1963), 32–48.Google Scholar
[2]Rosen, W. G., ‘On invariant means over compact semigroups’, Proc. Amer. Math. Soc. 7 (1956), 1076–1082.CrossRefGoogle Scholar
[3]Wilde, C., Jayachandran, T., ‘Amenable transformation Semigroups’, J. Australian Math. Soc., v XII (1971), 502–510.CrossRefGoogle Scholar
[4]Wilde, C., Witz, K., ‘Invariant means and the Stone-Cech compactification,’ Pacific J.Math. 21 (1967), 577–586.CrossRefGoogle Scholar