Abstract

Given reduced amalgamated free products of C^*-algebras (A,φ) = (A_ι,φ_ι) and (D,ψ) = (D_ι,ψ_ι), an embedding A↪D is shown to exist assuming there are conditional–expectation–preserving embeddings A_ι↪D_ι. This result is extended to show the existence of the reduced amalgamated free product of certain classes of unital completely positive maps. Finally, analogues of the above mentioned results are proved for amagamated free products of von Neumann algebras.

Authors