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Lattice Dilations of Positive Contractions on Lp-Spaces

Published online by Cambridge University Press:  20 November 2018

Rainer Nagel  and
Günther Palm
Rainer Nagel
Affiliation:
Mathematisches Institut der Universität, Auf der Morgenstelle 10, 7400 Tübingen
Günther Palm
Affiliation:
Max-Planck-Institut für Biologische Kybernetik, Spemannstr. 38, 7400 Tübingen
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Abstract

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In the spirit of our previous paper (Math. Z. 156, 265 - 277 (1977)) we present a functional analytic proof of the following result of M. A. Akcoglu: Every positive contraction on a reflexive Lp-space has a lattice dilation.

Keywords

47A3547B55
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 25 , Issue 3 , 01 September 1982 , pp. 371 - 374
Copyright
Copyright © Canadian Mathematical Society 1982

References

1. Akcoglu, M. A., A pointwise ergodic theorem in Lp-spaces. Canadian J. Math. 27, (1975), 1075-1082.Google Scholar
2. Akcoglu, M. A., Positive contractions of L1-spaces. Math. Z. 143, (1975), 5-13.Google Scholar
3. Akcoglu, M. A. and Kopp, P. E., Construction of dilations of positive Lp-contractions. Math. Z. 155, (1977), 119-127.Google Scholar
4. Akcoglu, M. A. and Sucheston, L., Dilations of positive contractions on Lp-spaces. Canadian Math. Bull. 20, (1977), 285-292.Google Scholar
5. Kern, M., Nagel, R. and Palm, G., Dilations of positive operators: construction and ergodic theory. Math. Z. 156, (1977), 265-277.Google Scholar
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