The stable rank of some free product C*-algebras

Details The stable rank of some free product C*-algebras The stable rank of some free product C*-algebras

1996-08-09

arxiv.org/abs/funct-an/9608001v2

Mathematics

Operator Algebras

30 pages, Latex. This revision includes an extra section where the special case of the reduced C*-algebra of the free group on

Scientific paper

It is proved that the reduced group C*-algebra C*_{red}(G) has stable rank one (i.e. its group of invertible elements is a dense subset) if G is a discrete group arising as a free product G_1*G_2 where |G_1|>=2 and |G_2|>=3. This follows from a more general result where it is proved that if (A,tau) is the reduced free product of a family (A_i,tau_i), i\in I, of unital C*-algebras A_i with normalized faithful traces tau_i, and if the family satisfies the Avitzour condition (i.e. the traces, tau_i, are not too lumpy in a specific sense), then A has stable rank one.

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