We present an improved version of commutatormethods for unitary operators under a weak regularity condition. Once applied to a unitary operator, the method typically leads to the absence of singularly continuous spectrum and to the local finiteness of point spectrum. Large families of locally smooth operators are also exhibited. Half of the paper is dedicated to applications, and a special emphasis is put on the study of cocycles over irrational rotations. It is apparently the first time that commutator methods are applied in the context of rotation algebras, for the study of their generators.
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Claudio Fernández, Serge Richard, Rafael Tiedra de Aldecoa, Commutator methods for unitary operators. J. Spectr. Theory 3 (2013), no. 3, pp. 271–292DOI 10.4171/JST/45