Property (T) for non-unital C*-algebras

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).

arXiv comment7 pages; to appear in J. Math. Anal. Appl

References in corpus (1)

• Kazhdan's Property T and C*-algebras

Cited by in corpus (2)

• A property for locally convex ${}^{\ast }$-algebras related to Property $(T)$ and character amenability
• Property (T) for locally compact groups and C*-algebras