Entropy in type I algebras

It is shown that if (M,φ,α) is a W∗-dynamical system with M a type I von Neumann algebra then the entropy of α w.r.t. φ equals the entropy of the restriction of α to the center of M. If furthermore (N,ψ, β) is a W∗-dynamical system with N injective then hφ⊗ψ(α ⊗ β) = hφ(α) + hψ(β). 1. Introduction. In the theory of non-commutative entropy the attention has almost exclu-sively been concentrated on non-type I algebras. We shall in the present paper remedy this situation by proving the basic facts on entropy of auto-morphisms of type I C∗- and von Neumann-algebras. The results are as nic