## 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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