The maximum unitary rank of some \(C^*\)-algebras. (English) Zbl 0661.46052

Putnam, Ian F.; Rørdam, Mikael

Math. Scand. 63, No. 2, 297-304 (1988).

It is proved that not all elements in the unit ball of certain \(C^*\)- algebras (infinite dimensional separable abelian \(C^*\)-algebras, infinite dimensional AF-algebras, irrational rotation \(C^*\)-algebras, and the reduced group \(C^*\)-algebra of the free group of n generators) can be written as the mean of two unitary elements in the algebra. Thus the maximum unitary rank of these algebras is either 3 or \(\infty\).

Reviewer: M.Rørdam

MSC:

46L05

General theory of \(C^*\)-algebras

Keywords:

infinite dimensional separable abelian \(C^*\)-algebras; infinite dimensional AF-algebras; irrational rotation \(C^*\)-algebras; reduced group \(C^*\)-algebra of the free group of n generators