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.
Cite this article
Marie Choda, Reduced Free Products of Completely Positive Maps and Entropy for Free Product of Automorphisms. Publ. Res. Inst. Math. Sci. 32 (1996), no. 2, pp. 371–382DOI 10.2977/PRIMS/1195162968