Hostname: page-component-7dd5485656-zklqj Total loading time: 0 Render date: 2025-10-31T20:46:16.982Z Has data issue: false hasContentIssue false
  • English
  • Français

A Dominated Ergodic Theorem for Contractions with Fixed Points

Published online by Cambridge University Press:  20 November 2018

A. De La Torre
A. De La Torre*
Affiliation:
Department of Mathematics McGill University Montreal, Quebec Canada
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 be a finite measure space, and let T be a contraction in real Lp (X). (i.e. T is linear and ||T||≤1). It is said that the Dominated Ergodic Theorem holds for T, if there exists a constant cp such that, if M(T)f(x) = supn 1/n then ||M(T)f||p ≤ cp ||f||p for every f in Lp .

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 20 , Issue 1 , 01 March 1977 , pp. 89 - 91
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Akcoglu, M. A., A pointwise ergodic theorem in Lp-spaces, Can. J. Math., 27 (1975), 1075-1082.Google Scholar
2. Burkholder, D. L., Semi Gaussian subspaces, Trans. Amer. Math. Soc. 104 (1962), 123-131.Google Scholar
3. Dundford, N. and Schwartz, J. T., Convergence almost everywhere of operator averages, J. Math. Mech. 5 (1956), 129-178.Google Scholar
4. Hopf, E., On the ergodic theorem for positive linear operators, J. Reine Angew, Math. 205 (1960), 101-106.Google Scholar
5. McGrath, S. A. J., An abelian ergodic theorem for semigroups in Lp space, Proc. Amer. Math. Soc. 54 (1976), 231-236.Google Scholar