Commutator methods for unitary operators
Mathematical Physics
2011-12-02 v1 Functional Analysis
math.MP
Spectral Theory
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 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.
Cite
@article{arxiv.1112.0167,
title = {Commutator methods for unitary operators},
author = {C. Fernandez and S. Richard and R. Tiedra de Aldecoa},
journal= {arXiv preprint arXiv:1112.0167},
year = {2011}
}
Comments
15 pages