Embeddings of reduced free products of operator algebras

Citation
Ef. Blanchard et Kj. Dykema, Embeddings of reduced free products of operator algebras, PAC J MATH, 199(1), 2001, pp. 1-19
Citations number
22
Categorie Soggetti
Mathematics
Journal title
PACIFIC JOURNAL OF MATHEMATICS
ISSN journal
00308730 → ACNP
Volume
199
Issue
1
Year of publication
2001
Pages
1 - 19
Database
ISI
SICI code
0030-8730(200105)199:1<1:EORFPO>2.0.ZU;2-G
Abstract
Given reduced amalgamated free products of C*-algebras (A,phi) = *(l is an element ofI)(A(l), phi (l)) and (D,psi) = *(l is an element ofI)(D-l, psi ( l)), an ambedding A curved right arrow D is shown to exist assuming there a re conditional expectation preserving embeddings A(l) curved right arrow D- l. This result is extended to show the existence of the reduced amalgamated free product of certain classes of unital completely positive maps. Finall y, analogues of the above mentioned results are proved for amagamated free products of von Neumann algebras.