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

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
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