Field algebras in quantum theory with indefinite metric. III. Spectrum of modular operator and Tomita's fundamental theorem

The construction of a modular theory for weakly closed J-involutive algebras of bounded operators on Pontryagin spaces is continued. The spectrum of the modular operator ..delta.. of such an algebra is investigated, the existence of a strongly continuous J-unitary group is established and, under the condition that the spectrum lies in the right half-plane, Tomita's fundamental theorem is proved.