Bulletin of the London Mathematical Society: Volume 38 -

PROPERTY (T) FOR C*-ALGEBRAS
BACHIR BEKKA
Published online by Cambridge University Press:

20 September 2006, pp. 857-867
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A notion of Property (T) is defined for an arbitrary unital C*-algebra $A$ admitting a tracial state. This is extended to a notion of Property (T) for a pair $(A,B),$ where $B$ is a C*-subalgebra of $A.$ Let $\Gamma$ be a discrete group and ${C}^*_{\rm r}(\Gamma)$ its reduced algebra. We show that $C^*_{\rm r}(\Gamma)$ has Property (T) if and only if the group $\Gamma$ has Property (T). More generally, given a subgroup $\Lambda$ of $\Gamma$, the pair $(C^*_{\rm r}(\Gamma),C^*_{\rm r}(\Lambda)) $ has Property (T) if and only if the pair of groups $(\Gamma, \Lambda)$ has Property (T).

PRIZEWINNERS 2006
Published online by Cambridge University Press:

20 September 2006, pp. 873-880
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Professor Sir Henry Peter Francis Swinnerton-Dyer Bt., KBE, FRS, of the University of Cambridge, is awarded the Pólya Prize.

Bulletin of the London Mathematical Society