Abstract
A generalization of the GNS construction to hermitian linear functionals W defined on a unital *-algebra is considered. Along these lines, a continuity condition (H) upon W is introduced such that (H) proves to be necessary and sufficient for the existence of a J-representation on a Krein space . The property whether or not the Gram operator J leaves the (common and invariant) domain of the representation invariant is characterized as well by properties of the functional W as by those of . Furthermore, the interesting class of positively dominated functionals is introduced and investigated. Some applications to tensor algebras are finally discussed.
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