N Dilations and Transference for Continuous One-Parameter Semigroups of Positive Contractions on ${\mathcal{L}}^p$-spaces

Abstract

These are the notes of a lecture given at the university of Wroclaw in 1996. We present results of semigroups of (sub)positive contractions on L^p-spaces. The dilation theorem of Akcoglue and sucheston is considered as a starting point. We construct a dilation of a strongly continuous semigroup of (sub)positive contractions on L^p-space, 1<p<infinity by a strongly continuous group of invertible isometries acting on some larger L^p-space. The transference results, for functions of the generators, are established as well as some square and maximal functions. This applies especially to sub-markovian semigroups.

Annales Universitatis Saraviensis, Series Mathematicae vol. 9, No. 1,1998