On spectral approximation, F{\o}lner sequences and crossed products
Abstract
In this article we study Foelner sequences for operators and mention their relation to spectral approximation problems. We construct a canonical Foelner sequence for the crossed product of a discrete amenable group with a concrete C*-algebra A with a Foelner sequence. We also state a compatibility condition for the action of on A. We illustrate our results with two examples: the rotation algebra (which contains interesting operators like almost Mathieu operators or periodic magnetic Schr\"odinger 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.
Keywords
Cite
@article{arxiv.1008.1151,
title = {On spectral approximation, F{\o}lner sequences and crossed products},
author = {Fernando Lledó},
journal= {arXiv preprint arXiv:1008.1151},
year = {2013}
}
Comments
15 pages; article partly rewritten, version to appear in J. Approx. Theory; changes w.r.t. v1: new introduction, results put in the context of spcetral approximation problems, only C*-crossed products are considered (instead of von Neumann crossed products; Eq.(3.6) of v1 deleted); more examples considered