Silbermann, Bernd : C^*-algebras and asymptotic spectral theory

Author(s):

Silbermann, Bernd

Title:

C^*-algebras and asymptotic spectral theory

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 11, 2007

Mathematics Subject Classification:

Abstract:

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.

Keywords:

Language:

English

Publication time:

2007