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The (**)-Haagerup property for C*-algebras

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Abstract

Extending the notion of Haagerup property for finite von Neumann algebras to the general von Neumann algebras, the authors define and study the (**)-Haagerup property for C*-algebras in this paper. They first give an answer to Suzuki’s question (2013), and then obtain several results of (**)-Haagerup property parallel to those of Haagerup property for C*-algebras. It is proved that a nuclear unital C*-algebra with a faithful tracial state always has the (**)-Haagerup property. Some heredity results concerning the (**)-Haagerup property are also proved.

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Correspondence to Xiaochun Fang.

Additional information

This work was supported by the National Natural Science Foundation of China (No. 11371279) and the Shandong Provincial Natural Science Foundation of China (No. ZR2015PA010).

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Li, C., Fang, X. The (**)-Haagerup property for C*-algebras. Chin. Ann. Math. Ser. B 37, 367–372 (2016). https://doi.org/10.1007/s11401-016-0958-4

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  • DOI: https://doi.org/10.1007/s11401-016-0958-4

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