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Topics in Operator Theory pp 223–252Cite as

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

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Part of the book series: Operator Theory: Advances and Applications ((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.

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Author information

Authors and Affiliations

  1. Department of Aeronautics and Astronautics Purdue, University, West Lafayette, IN, 47907, USA

    A. E. Frazho

  2. Afdeling Wiskunde Faculteit der Exacte Wetenschappen, Vrije Universiteit, De Boelelaan 1081a, NL-1081 HV, Amsterdam, The Netherlands

    M. A. Kaashoek

Authors
  1. A. E. Frazho
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  2. M. A. Kaashoek
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Additional information

Dedicated to Israel Gohberg, on the occasion of his 80th birthday, in friendship, with gratitude and admiration.

Communicated by V. Bolotnikov.

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Frazho, A.E., Kaashoek, M.A. (2010). A Contractive Operator View on an Inversion Formula of Gohberg-Heinig. In: Topics in Operator Theory. Operator Theory: Advances and Applications, vol 202. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0158-0_11

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