Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-14T05:14:03.181Z Has data issue: false hasContentIssue false
  • English
  • Français

On Finite Invariant Measure for Semigroups of Operators

Published online by Cambridge University Press:  20 November 2018

Usha Sachdevao
Usha Sachdevao*
Affiliation:
Ohio State University, Columbus, Ohio
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.

Let Σ be a left amenable semigroup, and let {Tσ: σ ∊ Σ} be a representation of Σ as a semigroup of positive linear contraction operators on L1(X, , p). This paper is devoted to the study of existence of a finite equivalent invariant measure for such semigroups of operators.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 2 , June 1971 , pp. 197 - 206
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Day, M. M., Amenable semigroups, Illinois J. Math. 1 (1957), 509-544.Google Scholar
2. Dean, D. W. and Sucheston, L., On invariant measures for operators, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 6 (1966), 1-9.Google Scholar
3. Dowker, Y. N., Finite and σ-finite invariant measures, Ann. of Math. 54 (1951), 595-608.Google Scholar
4. Granirer, E., On finite equivalent invariant measure for semi-groups of transformations, Duke Math. J. (to appear).Google Scholar
5. Hajian, A. B. and Ito, Y., Weakly wandering sets and invariant measures for a group of transformations, J. Math. Mech. 18 (1969), 1203-1216.Google Scholar
6. Hajian, A. B. and Kakutani, S., Weakly wandering sets and invariant measures, Trans. Amer. Math. Soc. 110 (1964), 136-151.Google Scholar
7. Lloyd, S. P., A mixing condition for extreme left invariant means, Trans. Amer. Math. Soc. 125(1966),461-481.Google Scholar
8. Natarajan, S., Invariant measures for families of transformations, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete (to appear).Google Scholar
9. Neveu, J., Mathematical foundations of the calculus of probability, Holden-Day, San Francisco, 1965.Google Scholar
10. Neveu, J., Existence of bounded invariant measures in Ergodic theory, Proc. of the Fifth Berkeley Symp., Vol. 2, pt. 2, 461-472.Google Scholar
11. Sucheston, L., An ergodic application of almost convergent sequences, Duke Math. J. 30 (1963),417-422.Google Scholar
12. Sucheston, L., On existence of finite invariant measures, Math. Z. 86 (1964), 327-336.Google Scholar