Unital Full Amalgamated Free Products of MF Algebras

Details Unital Full Amalgamated Free Products of MF Algebras Unital Full Amalgamated Free Products of MF Algebras

2010-06-12

arxiv.org/abs/1006.2447v1

Mathematics

Operator Algebras

Scientific paper

In this paper, we consider the question whether a unital full free product of MF algebras with amalgamation over a finite dimensional C*-algebra is an MF algebra. First, we show that, under a natural condition, a unital full free product of two separable residually finite dimensional (RFD) C*-algebras with amalgamation over a finite dimensional C*-algebra is again a separable RFD C*-algebra. Applying this result on MF C*-algebras, we show that, under a natual condition, a unital full free product of two MF algebras is again an MF algebra. As an application, we show that a unital full free product of two AF algebras with amalgamation over an AF algebra is an MF algebra if there are faithful tracial states on each of these two AF algebras such that the restrictions on the common subalgebra agree.

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