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A Contractive Operator View on an Inversion Formula of Gohberg-Heinig

  • A. E. Frazho
  • M. A. Kaashoek
Part of the Operator Theory: Advances and Applications book series (OT, volume 202)

Abstract

This paper presents a contractive operator view on the inversion formula for finite Toeplitz operator matrices due to Gohberg-Heinig. The general setting that will be used involves a Hilbert space operator T and a contraction A such that the compression of T - A*TA to the orthogonal complement of the defect space of A is the zero operator. For such an operator T the analogue of the Gohberg-Heinig inversion formula is obtained. The main results are illustrated on various special cases, including Toeplitz plus Hankel operators and model operators.

Keywords

Gohberg-Heinig inversion formula Toeplitz operator matrices contractive operators Toeplitz plus Hankel operators compression of Toeplitz operators model operators Stein equation 

Mathematics Subject Classification (2000).

Primary 47A45 47A50 47B35 

Secondary 15A09

47A20 65F05 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2010

Authors and Affiliations

  • A. E. Frazho
    • 1
  • M. A. Kaashoek
    • 2
  1. 1.Department of Aeronautics and Astronautics PurdueUniversityWest LafayetteUSA
  2. 2.Afdeling Wiskunde Faculteit der Exacte WetenschappenVrije UniversiteitAmsterdamThe Netherlands

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