Eigenvalues and Eigenspaces of Quantum Dynamical Systems and Their Tensor Products

The paper deals with spectral properties of abelian dynamical semigroups on von Neumann algebras. The notions of an eigenvalue and eigenspace for such semigroups are defined, generalizing those known for the classical case, and the existence of normal projections on the eigenspaces is proved. A more detailed study of properties of these projections is performed. Also spectral properties of tensor products of completely positive dynamical semigroups are investigated.