Embeddings of reduced free products of operator algebras

Etienne F. Blanchard and Kenneth J. Dykema

Vol. 199 (2001), No. 1, 1–19

DOI: 10.2140/pjm.2001.199.1

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.

Milestones

Received: 10 June 1999

Revised: 29 September 2000

Published: 1 May 2001