Geodesic
On Unital Full Amalgamated Free Products of Quasidiagonal $C^*$-Algebras
Funkcionalʹnyj analiz i ego priloženiâ, Tome 50 (2016) no. 1, pp. 47-58

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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.
Mots-clés : quasidiagonal $C^*$-algebra
Keywords: unital full amalgamated free product of $C^*$-algebras. 
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     author = {Qihui Li and Don Hadwin and Jiankui Li and Xiujuan Ma and Junhao Shen},
     title = {On {Unital} {Full} {Amalgamated} {Free} {Products} of {Quasidiagonal} $C^*${-Algebras}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {47--58},
     publisher = {mathdoc},
     volume = {50},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2016_50_1_a3/}
}
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Qihui Li; Don Hadwin; Jiankui Li; Xiujuan Ma; Junhao Shen. On Unital Full Amalgamated Free Products of Quasidiagonal $C^*$-Algebras. Funkcionalʹnyj analiz i ego priloženiâ, Tome 50 (2016) no. 1, pp. 47-58. http://geodesic.mathdoc.fr/item/FAA_2016_50_1_a3/