Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4590023 | Journal of Functional Analysis | 2014 | 40 Pages |
Abstract
A C⁎C⁎-algebra is called primitive if it admits a faithful and irreducible ⁎-representation. We show that if A1A1 and A2A2 are separable, unital, residually finite dimensional C⁎C⁎-algebras satisfying (dim(A1)−1)(dim(A2)−1)≥2(dim(A1)−1)(dim(A2)−1)≥2, then the unital C⁎C⁎-algebra full free product, A=A1⁎A2A=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⁎w⁎-dense in the state space.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Ken Dykema, Francisco Torres-Ayala,