On spectral approximation, Folner sequences and crossed products

In this article we study Folner sequences for operators and mention their relation to spectral approximation problems. We construct a canonical Folner sequence for the crossed product of a discrete amenable group Gamma with a concrete C*-algebra A with a Folner sequence. We also state a compatibility condition for the action of Gamma on A. We illustrate our results with two examples: the rotation algebra (which contains interesting operators like almost Mathieu operators or periodic magnetic Schrodinger 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. (C) 2012 Elsevier Inc. All rights reserved.