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

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

2007-10-30

arxiv.org/abs/0710.5605v1

Mathematics

Operator Algebras

7 pages; to appear in J. Math. Anal. Appl

Scientific paper

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).

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