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arXiv · 1201.4892

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

Ken Dykema·Francisco Torres-Ayala
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Abstract

A C*-algebra is called primitive if it admits a faithful and irreducible *-representation. We show that if A_1 and A_2 are separable, unital, residually finite dimensional C*-algebras that are not both two dimensional, then their unital C*-algebra full free product, A = A_1*A_2, is primitive. It follows that A is antiliminal and the set of pure states is w*-dense in the state space.

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Ken Dykema, Francisco Torres-Ayala. 2012-06-21. Primitivity of unital full free products of residually finite dimensional C*-algebras. https://arxiv.org/abs/1201.4892

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