AF embeddings and the numerical computation of spectra in irrational rotation algebras

• Autores: Nathanial P. Brown
• Localización: Numerical functional analysis and optimization, ISSN 0163-0563, Vol. 27, Nº 5-6, 2006, págs. 517-528
• Idioma: inglés
• DOI: 10.1080/01630560600790785
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• Resumen

  • A natural problem at the interface of operator theory and numerical analysis is that of finding a (finite dimensional) matrix whose eigenvalues approximate the spectrum of a given (infinite dimensional) operator. It is well-known that classical work of Pimsner and Voiculescu produces explicit matrix models for an interesting class of nontrivial examples (e.g., many discretized one-dimensional Schrödinger operators). In this paper, we observe that the spectra of their models (often) converge in the strongest possible sense - in the Hausdorff metric - and demonstrate that the rate of convergence is, in general, best possible