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Singular Integral Operators and Related Topics pp 295–303Cite as

Asymptotic Invertibility of Toeplitz Operators

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Part of the book series: Operator Theory Advances and Applications ((OT,volume 90))

Abstract

The purpose of this lecture is to exemplify with Toeplitz operators some ideas behind recent methods for studying stability of operator sequences and related problems. We demonstrate that several notions, strategies, and techniques commonly employed in operator theory have useful analogues in numerical analysis. In particular, we discuss a “symbol calculus” for sequences of finite sections of Toeplitz operators and embark on its consequences for the asymptotic behavior of the pseudospetra and the Moore-Penrose inverses of large truncated Toeplitz matrices.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Technical University Chemnitz-Zwickau, D - 09107, Chemnitz, Germany

    Bernd Silbermann

Authors
  1. Bernd Silbermann
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Editor information

Editors and Affiliations

  1. School of Mathematical Sciences, Tel-Aviv University, Ramat Aviv, Israel

    I. Gohberg

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© 1996 Birkhäuser Verlag, Basel/Switzerland

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Silbermann, B. (1996). Asymptotic Invertibility of Toeplitz Operators. In: Böttcher, A., Gohberg, I. (eds) Singular Integral Operators and Related Topics. Operator Theory Advances and Applications, vol 90. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9040-3_11

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  • DOI: https://doi.org/10.1007/978-3-0348-9040-3_11

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-9881-2

  • Online ISBN: 978-3-0348-9040-3

  • eBook Packages: Springer Book Archive

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