Hilbert C*-systems for actions of the circle group

Abstract

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