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A note on inner quasidiagonal C*-algebras


Authors: Qihui Li and Ze Li
Journal: Proc. Amer. Math. Soc. 144 (2016), 4861-4872
MSC (2010): Primary 46L09, 46L35
DOI: https://doi.org/10.1090/proc/13109
Published electronically: April 25, 2016
MathSciNet review: 3544535
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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.


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Additional Information

Qihui Li
Affiliation: Department of Mathematics, East China University of Science and Technology, Meilong Road 130, 200237 Shanghai, People’s Republic of China
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

DOI: https://doi.org/10.1090/proc/13109
Keywords: Inner quasidiagonal C*-algebras, unital full free products of C*-algebras, unital full amalgamated free products of C*-algebras.
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
Article copyright: © Copyright 2016 American Mathematical Society