On spectral approximation, Følner sequences and crossed products
-
Autores: Fernando Lledó
- Localización: Journal of approximation theory, ISSN 0021-9045, Vol. 170, Nº 1, 2013, págs. 155-171
- Idioma: inglés
- DOI: 10.1016/j.jat.2012.10.003
- Enlaces
-
Resumen
In this article we study F©ªlner sequences for operators and mention their relation to spectral approximation problems. We construct a canonical F©ªlner sequence for the crossed product of a discrete amenable group ¥Ã with a concrete C.-algebra A with a F©ªlner sequence. We also state a compatibility condition for the action of ¥Ã 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.
