Primitivity of unital full free products of residually finite dimensional C-algebras Academic Article

abstract

• 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.

authors

• Dykema, Kenneth

published proceedings

• Journal of Functional Analysis

author list (cited authors)

• Dykema, K., & Torres-Ayala, F.

citation count

• 1

complete list of authors

• Dykema, Ken||Torres-Ayala, Francisco

publication date

• December 2014

publisher

• Elsevier  Publisher

published in

• Journal of Functional Analysis  Journal

keywords

• C*-algebras
• Full Free Products
• Primitivity

Digital Object Identifier (DOI)

• 10.1016/j.jfa.2014.07.022

URI

• https://hdl.handle.net/1969.1/ETD-TAMU-2012-05-10887

start page

• 4519

end page

• 4558

volume

• 267

issue

• 11

URL

• http://dx.doi.org/10.1016/j.jfa.2014.07.022