A note on inner quasidiagonal C*-algebras
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- by Qihui Li and Ze Li
- Proc. Amer. Math. Soc. 144 (2016), 4861-4872
- DOI: https://doi.org/10.1090/proc/13109
- Published electronically: April 25, 2016
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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.References
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Bibliographic Information
- Qihui Li
- Affiliation: Department of Mathematics, East China University of Science and Technology, Meilong Road 130, 200237 Shanghai, People’s Republic of China
- MR Author ID: 940848
- Email: qihui_li@126.com
- Ze Li
- Affiliation: College of Science, Xi’an Polytechnic University, South Jinhua Road 19, 710048, Xi’an, People’s Republic of China
- Email: lize2001@126.com
- Received by editor(s): March 30, 2015
- Received by editor(s) in revised form: October 12, 2015, and January 18, 2016
- Published electronically: April 25, 2016
- Additional Notes: The research of the first author was supported by the National Natural Science Foundation of China
- Communicated by: Adrian Ioana
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 4861-4872
- MSC (2010): Primary 46L09, 46L35
- DOI: https://doi.org/10.1090/proc/13109
- MathSciNet review: 3544535