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Dilations of one Parameter Semigroups of Positive Contractions on Lp Spaces

Published online by Cambridge University Press:  20 November 2018

Gero Fendler
Gero Fendler*
Affiliation:
Fachbereich 9 Mathematik, Universität des Saarlandes, Postfach151151 D-66041 Saarbrücken, Germany e-mail: fendler@math.uni-sb.de
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Abstract

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It is proved in this note, that a strongly continuous semigroup of (sub)positive contractions acting on an Lp-space, for 1 < p < ∞ p ≠ 2, can be dilated by a strongly continuous group of (sub)positive isometries in a manner analogous to the dilation M. A. Akçoglu and L. Sucheston constructed for a discrete semigroup of (sub)positive contractions. From this an improvement of a von Neumann type estimation, due to R. R.Coifman and G.Weiss, on the transfer map belonging to the semigroup is deduced.

Keywords

47D0322D1243A22
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 49 , Issue 4 , 01 August 1997 , pp. 736 - 748
Copyright
Copyright © Canadian Mathematical Society 1997

References

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