Hilbert C*-systems for actions of the circle group

The paper contains constructions of Hilbert systems for the action of the c ircle group T using subgroups of implementable Bogoljubov unitaries w.r.t. Fock representations of the Fermion algebra for suitable data of the selfdu al framework:H is the reference Hilbert space, Gamma the conjugation and P a basis projection on H. The group C(spec Z --> T) of T-valued functions on spec Z turns out to be isomorphic to the stabilizer of A. In particular, e xamples are presented where the center Z of the fixed point algebra A, can be calculated explicitly.