Operator Semigroup Compactifications

Abstract

A weakly continuous, equicontinuous representation of a semitopological semigroup S S on a locally convex topological vector space X X gives rise to a family of operator semigroup compactifications of S S , one for each invariant subspace of X X . We consider those invariant subspaces which are maximal with respect to the associated compactification possessing a given property of semigroup compactifications and show that under suitable hypotheses this maximality is preserved under the formation of projective limits, strict inductive limits and tensor products.