  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.
