On spectral approximation, Følner 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 $\Gamma$ with a concrete C*-algebra A with a Foelner 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 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.

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

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• The role of C*-algebras in infinite dimensional numerical linear algebra
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Cited by in corpus (3)

• Amenability of coarse spaces and K-algebras
• F\olner sequences and finite operators
• A note on commutation relations and finite dimensional approximations