Primitivity of unital full free products of residually finite dimensional C⁎-algebras
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© 2014 Elsevier Inc. A C*-algebra is called primitive if it admits a faithful and irreducible *-representation. We show that if A1 and A2 are separable, unital, residually finite dimensional C*-algebras satisfying (dim(A1)-1)(dim(A2)-1)≥2, then the unital C*-algebra full free product, A=A1*A2, is primitive. It follows that A is antiliminal, it has an uncountable family of pairwise inequivalent irreducible faithful *-representations and the set of pure states is w*-dense in the state space.
author list (cited authors)
Dykema, K., & Torres-Ayala, F.
complete list of authors
Dykema, Ken||Torres-Ayala, Francisco