**-Haagerup Property for C*-Algebras |
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Authors: | C J Li and X C Fang |
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Institution: | 1. School of Mathematical Sciences, Shandong Normal University, Jinan 250014, China;2. Department of Mathematics, Tongji University, Shanghai 200092, China |
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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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Keywords: | $C^{*}$-algebras Von Neumann algebras Haagerup property |
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