New holomorphically closed subalgebras of $C^{\ast }$-algebras of hyperbolic groups

Abstract

We construct dense, unconditional subalgebras of the reduced group $C^{\ast }$-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 $C^{\ast }$-algebras and to delocalized $L^2$-invariants of negatively curved manifolds are given.