An illustrative example of the results presented in this paper is the following one. Let M be a compact C-manifold and φ a diffeomorphism of M for which
  1. (a)

    at least one point x 0X has a dense orbit {φ n x 0 : nZ};

  2. (b)

    every function f ∈ C(X, C) has a bounded orbit {f o φ n : nZ}



Compact Abelian Group Dense Orbit Uniform Topology Hilbert Base Ergodic System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    N. Dunford and J. T. Schwartz, Linear Operators, Part I : General Theory. Interscience Publ.Inc., New York 1958.Google Scholar
  2. [2]
    P. R. Halmos, Lectures on ergodic theory. Publications of the Math. Soc. of Japan 3 (1956).Google Scholar
  3. [3]
    R. A. Hirschfeld, Généralisation d’un théorème de M. Stone sur les groupes unitaires .C. R. Acad.Sci. Paris 264 (1967), 391–393.Google Scholar
  4. [4]
    R. A. Hirschfeld, Décomposition spectrale des représentations non unitaires, ibid. 266 (1968), 333–335.Google Scholar
  5. [5]
    R. A. Hirschfeld, Non-unitary representations, I. Spectral decomposition. Acta Math, (to appear).Google Scholar
  6. [6]
    S. Krein and M. Krein, On an internal characterization of the set of all continuous functions defined on a bicompact Hausdorff space. Dokl. Acad. Nauk SSSR 27 (1940), 427–430.Google Scholar
  7. [7]
    J. C. Oxtoby, Ergodic sets. Bull. Amer. Math. Soc. 58 (1952), 116–136.CrossRefGoogle Scholar
  8. [8]
    B. Walsh, Structure of spectral measures on locally convex spaces. Transact. Amer. Math. Soc. 120 (1965), 295–326.CrossRefGoogle Scholar

Copyright information

© Springer Basel AG 1969

Authors and Affiliations

  • R. A. Hirschfeld
    • 1
  1. 1.Mathematisch InstituutKatholieke UniversiteitNijmegenNederland

Personalised recommendations