Commutator methods for unitary operators

Fernandez, Claudio

Pontificia Universidad Católica de Chile

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Fernandez, Claudio Richard, Serge de Aldecoa, Rafael Tiedra

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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.

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Autor	Fernandez, Claudio Richard, Serge de Aldecoa, Rafael Tiedra
Título	Commutator methods for unitary operators
Revista	Journal of spectral theory
ISSN	1664-039X
ISSN electrónico	1664-0403
Volumen	3
Número de publicación	3
Página inicio	271
Página final	292
Fecha de publicación	2013
Resumen	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.
Derechos	acceso restringido
DOI	10.4171/JST/45
Enlace	https://doi.org/10.4171/JST/45 https://repositorio.uc.cl/handle/11534/101889
Id de publicación en WoS	WOS:000340039500002
Palabra clave	Unitary operators spectral analysis Mourre theory limiting absorption principle cocycles over rotations
Tipo de documento	artículo