Let {Mathematical expression} be a von Neumann algebra with the vector ω cyclic and separating for {Mathematical expression}. Let {Mathematical expression} be a group of unitary operators under which both ω and {Mathematical expression} are invariant. Let {Mathematical expression} (resp. ℜ′) be the fixed point algebra in 21 (resp. in {Mathematical expression}′). Let Fo be an orthogonal projection onto the subspace of all vectors invariant under {Mathematical expression}. It is shown that ℜ=( {Mathematical expression} ν {Fo})″ and that the irreducibility of ℜ implies that Fo is one-dimentional. Other consequences of the Theorem of Kovács and Szücs are also derived. In sec. 3. the spectrum properties of the group {Mathematical expression} are studied. It is proved that the point spectrum of {Mathematical expression} is symmetric and that it is a group provided ℜ is irreducible. In this case there exists a homomorphism χ→ {Mathematical expression} (resp. χ → {Mathematical expression}) of the point spectrum of {Mathematical expression} into the group of unitary operators in {Mathematical expression} (resp. in {Mathematical expression}′) uniquely (up to the phase) defined by {Mathematical expression}Vg=χ(g)Vg {Mathematical expression} (resp. the same for {Mathematical expression}). In sec. 4. the application of the foregoing results to the KMS-Algebra is given. © 1969 Springer-Verlag.
