11-184 Claudio Fernandez, Serge Richard and Rafael Tiedra

Commutator methods for unitary operators (511K, Postscript) Dec 1, 11

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Abstract. We present an improved version of commutator methods 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 fi niteness of point spectrum. Large families of locally smooth operators are also exhibited. Half of the paper is dedicated to applications, and a special emphasize is put on the study of cocycles over irrational rotations. It is apparently the fi rst time that commutator methods are applied in the context of rotation algebras, for the study of their generators.

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