Embeddings of reduced free products of operator algebras

Etienne Blanchard (1) , Kenneth Dykema (2)

1 IMJ - Institut de Mathématiques de Jussieu
2 TAMU - Department of Mathematics [Texas]

Given reduced amalgamated free products of C$^*$--algebras $(A,\phi)=\freeprodi(A_\iota,\phi_\iota)$ and $(D,\psi)=\freeprodi(D_\iota,\psi_\iota)$, an embedding $A\hookrightarrow D$ is shown to exist assuming there are conditional expectation preserving embeddings $A_\iota\hookrightarrow D_\iota$. This result is extended to show the existence of the reduced amalgamated free product of certain classes of unital completely positive maps. Finally, the reduced amalgamated free product of von Neumann algebras is defined in the general case and analogues of the above mentioned results are proved for von Neumann algebras.

Domaines: Algèbres d'opérateurs [math.OA]

Etienne Blanchard, Kenneth Dykema. Embeddings of reduced free products of operator algebras. Pacific J. Math., 2001, 199, pp.1--19. ⟨hal-00922864⟩