Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-26T05:41:29.970Z Has data issue: false hasContentIssue false
  • English
  • Français

Ergodic Properties of Lamperti Operators

Published online by Cambridge University Press:  20 November 2018

Charn-Huen Kan
Charn-Huen Kan*
Affiliation:
McGill University, Montreal, Quebec
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.

We shall assume throughout this paper, unless otherwise specified, that p is a fixed number, 1 < p < ∞.

It is well known that to prove the poin.twise ergodic convergence of a contraction T on an Lp-space it is enough to prove a Dominated Ergodic Estimate (DEE) for T (see e.g. [11]).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 6 , 01 December 1978 , pp. 1206 - 1214
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Akcoglu, M. A., A pointwise ergodic theorem inLp-spaces, Can. J. Math. 27 (1975), 1075–1082.Google Scholar
2. Akcoglu, M. A. and Sucheston, L., Remarks on dilations in Lp-spaces, Proc. A.M.S. 53 (1975), 80–82.Google Scholar
3. Banach, S., Théorie des opérations linéaires, Monogr. Mat., Tom 1, Warsaw, 1932.Google Scholar
4. Calderôn, A. P., Ergodic theory and translation-invariant operators, Proc. N.A.S. (51) (1968), 349–353.Google Scholar
5. Chacon, R. V. and Krengel, U., Linear modulus of a linear operator, Proc. A.M.S. 15 (19G4), 553–559.Google Scholar
6. Chacon, R. V. and McGrath, S. A., Estimates of positive contractions, Pacific J. Math. 30 (1969), 609–620.Google Scholar
7. Coifman, R. R. and Weiss, G., Operators associated with representations of amenable groups, singular integrals induced by ergodic flows, the rotation method a?id multipliers, Studia Math. 47 (1973), 285–303.Google Scholar
8. de la Torre, A., A simple proof of the maximal ergodic theorem, Can. J. Math. 28 (1976), 1073–1075.Google Scholar
9. Gantmacher, F. R., The theory of matrices, vol. 2 (Chelsea, New York, 1959).Google Scholar
10. Hardy, G. H. and Littlewood, J. E., A maximal theorem with function-theoretic applications, Acta Math. 5J+ (1930), 81–116.Google Scholar
11. Ionescu Tulcea, A., Ergodic properties of isometrics in Lp-spaces, 1 < p < co f Bull. A.M.S. 70 (1964), 366–371.Google Scholar
12. Lamperti, J., On the isometrics of certain function spaces, Pacific J. Math. 8 (1958), 459–466.Google Scholar