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Contributions to Operator Theory in Spaces with an Indefinite Metric pp 309–326Cite as

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Lyapunov stability of a perturbed multiplication operator

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Part of the book series: Operator Theory Advances and Applications ((OT,volume 106))

Abstract

The perturbation of the multiplication operator in the space L 2(0,1) by a Volterra operator with degenerate kernel is a particular case of the socalled “Friedrichs model”. We characterize the point spectrum of such a perturbation and establish a sharp result on the Lyapunov stability in the case that the kernel vanishes on the diagonal.

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Author information

Authors and Affiliations

  1. Department of Mathematical Physics, St.-Petersburg University, 198904, St. Petersburg, Russia

    S. N. Naboko

  2. Department of Mathematics, University of Regensburg, 93040, Regensburg, Germany

    C. Tretter

Authors
  1. S. N. Naboko
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  2. C. Tretter
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Groningen, P.O. Box 800, 9700 AV, Groningen, The Netherlands

    Aalt Dijksma

  2. School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, 69978, Israel

    Israel Gohberg

  3. Department of Mathematics, Free University, De Boelelaan, 1081a, 1081 HV, Amsterdam, The Netherlands

    Marinus A. Kaashoek

  4. NWF 1, Mathematics, University of Regensburg, Universitaetsstr. 31, D-93053, Regensburg, Germany

    Reinhard Mennicken

Additional information

Dedicated to Heinz Langer on the occasion of his sixtieth birthday

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© 1998 Springer Basel AG

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Naboko, S.N., Tretter, C. (1998). Lyapunov stability of a perturbed multiplication operator. In: Dijksma, A., Gohberg, I., Kaashoek, M.A., Mennicken, R. (eds) Contributions to Operator Theory in Spaces with an Indefinite Metric. Operator Theory Advances and Applications, vol 106. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8812-7_17

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  • DOI: https://doi.org/10.1007/978-3-0348-8812-7_17

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9782-2

  • Online ISBN: 978-3-0348-8812-7

  • eBook Packages: Springer Book Archive

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