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Linear and One-dimensional

  • Albrecht Böttcher

Abstract

The first time I encountered the name Gohberg was in 1978 when Bernd Silbermann told me about Gohberg’s invertibility criterion for infinite Toeplitz matrices. It says that such a matrix is invertible if and only if the function whose Fourier coefficients are the entries of the first row and first column does not have zeros on the unit circle and has winding number zero about the origin, provided, of course, that this function is continuous. I was deeply impressed by such a fascinating interplay of operator theory, harmonic analysis, and topology, and now, 30 years later, I have to state that this theorem by Gohberg has actually determined my entire mathematical career. In the late 1970s the three books by Israel Gohberg with Israel Feldman, Naum Krupnik, and Mark Krein occupied the most prominent place on my desk and introduced me to a world full of excitement and profound beauty.

Keywords

Toeplitz Operator Singular Integral Operator Toeplitz Matrice Olive Grove Prominent Place 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag AG 2008

Authors and Affiliations

  • Albrecht Böttcher
    • 1
  1. 1.Chemnitz

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