The simultaneous dilation of a
group of contractions on a Hilbert space by a group of isometries is generalized here
to operators on locally convex spaces. The basic construction, using a quotient of a
large direct sum, is found in the Hilbert space treatment. The particular difficulties
to be overcome and innovations introduced here relate to the definition of
contraction and isometry for operators on a locally convex space, and to
the handling of various topologies on the operators under scrutiny. With
these definitions the traditional dilation of a contraction by an isometry is
recovered. Finally we have a variation of the basic dilation theorem particularly
suited to semi-groups of operators on locally convex spaces and to spectral
operators.
