Representations of Hermitian Kernels¶by Means of Krein Spaces.¶II. Invariant Kernels

Abstract:

In this paper we study hermitian kernels invariant under the action of a semigroup with involution. We characterize those hermitian kernels that realize the given action by bounded operators on a Kreîn space. This is motivated by the GNS representation of *-algebras associated to hermitian functionals, the dilation theory of hermitian maps on C ^*-algebras, as well as others. We explain the key role played by the technique of induced Kreîn spaces and a lifting property associated to them.