A note on inner quasidiagonal C*-algebras

Li, Qihui; Li, Ze

doi:10.1090/proc/13109

A note on inner quasidiagonal C*-algebras
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by Qihui Li and Ze Li PDF

Proc. Amer. Math. Soc. 144 (2016), 4861-4872 Request permission

Abstract:

In this paper, we give two new characterizations of separable inner quasidiagonal C*-algebras. Based on these characterizations, we show that a unital full free product of two inner quasidiagonal C*-algebras is itself inner quasidiagonal. As an application, we show that a unital full free product of two inner quasidiagonal C*-algebras with amalgamation over a full matrix algebra is inner quasidiagonal. Meanwhile, we conclude that a unital full free product of two AF algebras with amalgamation over a finite-dimensional C*-algebra is inner quasidiagonal if there are faithful tracial states on each of these two AF algebras such that the restrictions of these states to the common subalgebra coincide.

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