Commutator methods for unitary operators
No Thumbnail Available
Date
2013
Journal Title
Journal ISSN
Volume Title
Publisher
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 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.
Description
Keywords
Unitary operators, spectral analysis, Mourre theory, limiting absorption principle, cocycles over rotations