Decompositions of a Krein space in regular subspaces invariant under a uniformly bounded C0-semigroup of bi-contractions

Abstract

We give necessary and sufficient conditions under which a C 0-semigroup of bi-contractions on a Krein space is similar to a semigroup of contractions on a Hilbert space. Under these and additional conditions we obtain direct sum decompositions of the Krein space into invariant regular subspaces and we describe the behavior of the semigroup on each of these summands. In the last section we give sufficient conditions for the co-generator of the semigroup to be power bounded.