New holomorphically closed subalgebras of $C^*$-algebras of hyperbolic groups

Details New holomorphically closed subalgebras of $C^*$-algebras of hyperbolic groups New holomorphically closed subalgebras of $C^*$-algebras of hyperbolic groups

2009-04-23

arxiv.org/abs/0904.3675v1

Mathematics

Operator Algebras

Scientific paper

We construct dense, unconditional subalgebras of the reduced group
$C^*$-algebra of a word-hyperbolic group, which are closed under holomorphic
functional calculus and possess many bounded traces. Applications to the cyclic
cohomology of group $C^*$-algebras and to delocalized $L^2$-invariants of
negatively curved manifolds are given.

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