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15. Property (T) for non-unital C∗-algebras

Author

Leung, Chi-Wai, Ng, Chi-Keung, and Wong, Ngai-Ching

Subjects
Mathematics - Functional Analysis, C∗-algebras, 46L, Property (T), Mathematics - Operator Algebras, FOS: Mathematics, Operator Algebras (math.OA), Functional Analysis (math.FA)
Abstract

Inspired by the recent work of Bekka, we study two reasonable analogues of property (T) for not necessarily unital C*-algebras. The stronger one of the two is called ``property (T)'' and the weaker one is called ``property (T_{e})''. It is shown that all non-unital C*-algebras do not have property (T) (neither do their unitalizations). Moreover, all non-unital $\sigma$-unital C*-algebras do not have property (T_e)., Comment: 7 pages; to appear in J. Math. Anal. Appl

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