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Funktsional'nyi Analiz i ego Prilozheniya, 2016, Volume 50, Issue 1, Pages 47–58
DOI: https://doi.org/10.4213/faa3214 (Mi faa3214) 		 
This article is cited in 2 scientific papers (total in 2 papers)

On Unital Full Amalgamated Free Products of Quasidiagonal $C^*$-Algebras

Qihui Lia, Don Hadwinb, Jiankui Lia, Xiujuan Mac, Junhao Shenb

a Department of Mathematics, East China University of Science and Technology, Shanghai, China
b Department of Mathematics, University of New Hampshire, Durham, USA
c Department of Mathematics, Hebei University of Technology, Tianjing, China
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DOI: https://doi.org/10.4213/faa3214
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.
Keywords: quasidiagonal $C^*$-algebra, unital full amalgamated free product of $C^*$-algebras.
Funding agency Grant number
National Natural Science Foundation of China 11201146
Chinese Universities Scientific Fund
Received: 02.08.2013
English version:
Functional Analysis and Its Applications, 2016, Volume 50, Issue 1, Pages 39–47
DOI: https://doi.org/10.1007/s10688-016-0126-3
Bibliographic databases:
Document Type: Article
UDC: 517.98
Language: Russian
Citation: Qihui Li, Don Hadwin, Jiankui Li, Xiujuan Ma, Junhao Shen, “On Unital Full Amalgamated Free Products of Quasidiagonal $C^*$-Algebras”, Funktsional. Anal. i Prilozhen., 50:1 (2016), 47–58; Funct. Anal. Appl., 50:1 (2016), 39–47
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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