Commutator methods for unitary operators | Zendy

Claudio Fernández | Zendy; Serge Richard | Zendy; Rafael Tiedra de Aldecoa | Zendy

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Commutator methods for unitary operators

Author(s) -

Claudio Fernández,

Serge Richard,

Rafael Tiedra de Aldecoa

Publication year - 2013

Publication title -

journal of spectral theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.063

H-Index - 19

eISSN - 1664-0403

pISSN - 1664-039X

DOI - 10.4171/jst/45

Subject(s) - commutator , unitary state , spectrum (functional analysis) , mathematics , operator (biology) , context (archaeology) , pure mathematics , irrational number , algebra over a field , point (geometry) , rotation (mathematics) , physics , quantum mechanics , geometry , paleontology , biochemistry , chemistry , lie conformal algebra , repressor , biology , political science , transcription factor , law , gene

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 emphasize 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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