Illinois Journal of Mathematics

A note on unital full amalgamated free products of RFD C-algebras

Qihui Li and Junhao Shen

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In the paper, we consider the question whether a unital full amalgamated free product of RFD (residually finite dimensional) C-algebras is RFD again. One example shows that the answer to the general case is no. We give a necessary and sufficient condition such that a unital full amalgamated free product of RFD C-algebras with amalgamation over a finite dimensional C-algebra is RFD. Applying this result, we conclude that a unital full free product of two same RFD C-algebras with amalgamation over a finite-dimensional C-algebra is always RFD.

Article information

Illinois J. Math., Volume 56, Number 2 (2012), 647-659.

First available in Project Euclid: 22 November 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46L09: Free products of $C^*$-algebras 46L35: Classifications of $C^*$-algebras


Li, Qihui; Shen, Junhao. A note on unital full amalgamated free products of RFD C ∗ -algebras. Illinois J. Math. 56 (2012), no. 2, 647--659. doi:10.1215/ijm/1385129969.

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