Dilations of one Parameter Semigroups of Positive Contractions on <i>L^p</i> Spaces

Abstract

Abstract It is proved in this note, that a strongly continuous semigroup of (sub)positive contractions acting on an L p -space, for 1 &lt; p &lt; ∞ 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.