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

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

2012-02-24

arxiv.org/abs/1202.5455v2

Mathematics

Operator Algebras

Version 2 includes a generalization of Theorem 3.1 based on the work of Pisier

Scientific paper

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.

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