Let α and β be *-automorphisms of a C*-algebra A such that α + α β + β-1. There exist invariant ideals I1I2 and I3 of A, with II ∩ I2 ∩ I3 = {O}, containing, respectively, the range ofβ − α, the range of β − α-1, and the union of the ranges of β2 − α2 and β2 − α-2. The induced actions on the quotient algebras give a decomposition of the system (A, α, β) into systems where β = α, β = α-2 and α2 = α-2.
If α and β are one-parameter groups of *-automorphisms such that α + α-1 = β + β−1, then the corresponding result is valid, and may be strengthened to assert that I1 ∩ I2 = {0}.
These results are analogues and extensions of similar results of A. B. Thaheem et al. for von Neumann algebras and commuting automorphisms.
