Embeddings of reduced free products of operator algebras

1999/11/02 by Etienne Blanchard, Blanchard, Etienne, Ken Dykema +1 · 2 citations
Mathematics · #FOS: Mathematics #Operator Algebras (math.OA) #math.OA

paper · pdf · doi:10.48550/arxiv.math/9911012

Revised version to appear in Pacific J. Math. 15 pages

arxiv created 2000/09/11 · arxiv updated 2009/11/30

Abstract

Given reduced amalgamated free products of C^*-algebras, (A,phi)=*_i(A_i,phi_i) and (D,psi)=*_i(D_i,psi_i), an embedding A→ D is shown to exist assuming there are conditional expectation preserving embeddings A_i→ D_i. This result is extended to show the existance of the reduced amalgamated free product of certain classes of unital completely positive maps. Analogues of the above mentioned results are proved for von Neumann algebras.

Cited by

• Selfless reduced free products and graph products of C^∗-algebras
• Proximality and selflessness for group C*-algebras

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