Skip to main content
Log in

Interpolation sets for subalgebras ofl (Z)

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

Abstract

LetU be the subalgegra ofl (Z) generated by the minimal functions. The collection ofU-interpolation sets is identified as the ideal of small subsets ofZ. General theorems about the relation between invariant ideals and collections ofA-interpolation sets, for subalgebrasA ofl , are proven.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. R. Ellis,Lectures on Topological Dynamics, Benjamin, New York, 1969.

    MATH  Google Scholar 

  2. H. Furstenberg,Disjointness in ergodic theory, minimal sets and a problem in diophantine approximation, Math. Syst. Theory1 (1967), 1–49.

    Article  MATH  MathSciNet  Google Scholar 

  3. H. Furstenberg,Recurrence in Ergodic Theory and Combinatorial Number Theory, Princeton University Press, Princeton, New Jersey, 1981.

    MATH  Google Scholar 

  4. H. Furstenberg and B. Weiss,Topological dynamics and combinatorial number theory, J. Analyse Math.34 (1978), 61–85.

    Article  MATH  MathSciNet  Google Scholar 

  5. S. Glasner,Proximal Flows, Lecture Notes in Math.517, Springer Verlag, 1976.

  6. S. Glasner,Divisible properties and the Stone-Čech compactification, Can. J. Math.32 (1980), 993–1007.

    MATH  MathSciNet  Google Scholar 

  7. W. Sierpinski,Fonctions additives, non complétement additives et fonction non measurable, Fundam. Math.33 (1938), 96–99.

    Google Scholar 

  8. W. A. Veech,Minimal sets and Souslin sets, inRecent Advances in Topological Dynamics (Proc. Conf., Yale Univ., 1972), Lecture Notes in Math.318, Springer Verlag, 1973, pp. 253–266.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Glasner, S., Weiss, B. Interpolation sets for subalgebras ofl (Z). Israel J. Math. 44, 345–360 (1983). https://doi.org/10.1007/BF02761993

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02761993

Keywords

Navigation