Abstract
In the paper, we consider the question as to whether a unital full amalgamated free product of quasidiagonal C*-algebras is itself quasidiagonal. We give a sufficient condition for a unital full amalgamated free product of quasidiagonal C*-algebras with amalgamation over a finite-dimensional C*-algebra to be quasidiagonal. By applying this result, we conclude that the unital full free product of two AF algebras with amalgamation over a finite-dimensional C*-algebra is AF if there exists a faithful tracial state on each of the two AF algebras such that the restrictions of these states to the common subalgebra coincide.
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The research of the first author is partially supported by National Natural Science Foundation of China (Grant No. 11201146) and the Fundamental Research Funds for the Central Universities as well as SRF for ROCS, SEM.
Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 50, No. 1, pp. 38–46, 2016
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Li, Q., Hadwin, D., Li, J. et al. On Unital Full Amalgamated Free Products of Quasidiagonal C*-Algebras. Funct Anal Its Appl 50, 39–47 (2016). https://doi.org/10.1007/s10688-016-0126-3
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DOI: https://doi.org/10.1007/s10688-016-0126-3