Reduced Free Products of Completely Positive Maps and Entropy for Free Product of Automorphisms

Abstract

The reduced free product of unital completely positive maps is defined. An invariant state on a C*-algebra for an automorphism (based on the free shift) is the composition of a state of a subalgebra with the reduced free product of expectations. Entropies for the reduced free product and the tensor product of an automorphism γ with the free shift coincide with the entropy of γ.