Dilations of one Parameter Semigroups of Positive Contractions on L p Spaces

It is proved in this note, that a strongly continuous semigroup of (sub)positive contractions acting on an L p -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...

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Bibliographic Details
Published in:Canadian journal of mathematics 1997-08, Vol.49 (4), p.736-748
Main Author: Fendler, Gero
Format: Article
Language:English
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Summary:It is proved in this note, that a strongly continuous semigroup of (sub)positive contractions acting on an L p -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.
ISSN:0008-414X
1496-4279
DOI:10.4153/CJM-1997-036-x