Silbermann, Bernd : C^*-algebras and asymptotic spectral theory
- C^*-algebras and asymptotic spectral theory
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- Preprint series:
- Technische UniversitÃ¤t Chemnitz, FakultÃ¤t fÃ¼r Mathematik (Germany). Preprint 11, 2007
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- The presented material is a slightly polished and extended version of lectures given at Lisbon, WOAT 2006. Three basic topics of numerical functional analysis are discussed: stability, fractality, and Fredholmness. It is further shown that these notions are corner stones in order to understand a few topics in asymptotic spectral theory: asymptotic behavior of singular values, $\varepsilon$-pseudospectra, norms. Four important examples are discussed: Finite sections of quasidiagonal operators, Toeplitz operators, band-dominated operators with almost periodic coefficients, and general band-dominated operators. The elementary theory of $C^*$-algebras serves as the natural background of these topics.
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