The stable rank of some free product C*-algebras
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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.
30 pages, Latex. This revision includes an extra section where the special case of the reduced C*-algebra of the free group on two generators is considered separately. This has the advantage of making the main ideas more transparent
30 pages, Latex. This revision includes an extra section where the special case of the reduced C*-algebra of the free group on two generators is considered separately. This has the advantage of making the main ideas more transparent