Which Eigenvalues Are Found by the Lanczos Method?
SIAM Journal on Matrix Analysis and Applications
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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 @C with a concrete C^*-algebra A with a Folner sequence. We also state a compatibility condition for the action of @C 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.