On spectral approximation, Følner sequences and crossed products

In this article we study Følner sequences for operators and mention their relation to spectral approximation problems. We construct a canonical Følner sequence for the crossed product of a discrete amenable group Γ with a concrete C∗-algebra A with a Følner sequence. We also state a compatibility co...

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Bibliographic Details
Published in:Journal of approximation theory 2013-06, Vol.170, p.155-171
Main Author: Lledó, Fernando
Format: Article
Language:English
Subjects:
Amenable groups
Crossed products
C∗-algebras
Følner sequences
Quasidiagonality
Rotation algebra
Spectral approximation
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Summary:In this article we study Følner sequences for operators and mention their relation to spectral approximation problems. We construct a canonical Følner sequence for the crossed product of a discrete amenable group Γ with a concrete C∗-algebra A with a Følner sequence. We also state a compatibility condition for the action of Γ on A. We illustrate our results with two examples: the rotation algebra (which contains interesting operators like almost Mathieu operators or periodic magnetic Schrödinger operators on graphs) and the C∗-algebra generated by bounded Jacobi operators. These examples can be interpreted in the context of crossed products. The crossed products considered can be also seen as a more general frame that included the set of generalized band-dominated operators.
ISSN:0021-9045
1096-0430
DOI:10.1016/j.jat.2012.10.003