On a Notion of Exactness for Reduced Free Products of C*-Algebras

Abstract

We will study some modifications to the notion of an exact C*-algebra by replacing the minimal tensor product with the reduced free product. First we will demonstrate how the reduced free product of a short exact sequence of C*-algebras with another C*-algebra may be taken. It will then be demonstrated that this operation preserves exact sequences. We will also establish that adjoining arbitrary k-tuples of operators in a free way behaves well with respect to taking ultrapowers.

Version 2 includes a generalization of Theorem 3.1 based on the work of Pisier, Version 3 corrects some minor typos

References in corpus (3)

• The norm of polynomials in large random and deterministic matrices
• Khintchine type inequalities for reduced free products and Applications
• A Kurosh type theorem for type II_1 factors

Cited by in corpus (1)

• Non-commutative rational function in strongly convergent random variables