On strong α-stability of invariant subspaces of matrices

  • A. C. M. Ran
  • L. Roozemond
Part of the Operator Theory: Advances and Applications book series (OT, volume 40)


Stability properties of invariant subspaces of matrices have been studied extensively the last decade. The first results on stability of invariant subspaces were obtained independently in 1979 by Campbell and Daughtry [CD] and Bart, Gohberg and Kaashoek [BGK]. Recently a complete theory on stability of invariant subspaces was laid down in a book by Gohberg, Lancaster and Rodman [GLR]. The development of this theory was chiefly done by mathematicians from the ‘Gohberg school’. Our aim in this paper is to add a little bit to this beautiful theory.


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  1. [BGK]
    Bart, H., Gohberg, I. and Kaashoek, M.A.: Minimal Factorization of Matrix and Operator Functions, Birkhäuser, Basel, 1979.Google Scholar
  2. [CD]
    Campbell, S. and Daughtry, J.: The stable solutions of quadratic matrix equations, Proc. AMS 74 (1979), 19–23.CrossRefGoogle Scholar
  3. [GLR]
    Gohberg, I., Lancaster, P. and Rodman, L.: Invariant Subspaces of Matrices with Applications, John Wiley & Sons, New York, 1986.Google Scholar
  4. [RR]
    Ran, A.C.M. and Rodman, L.: Stability of Invariant Lagrangian Subspaces I, in: Topics in Operator Theory, Constantin Apostol memorial issue, (ed: I. Gohberg), OT 32, Birkhäuser, Basel, 1988.Google Scholar

Copyright information

© Birkhäuser Verlag Basel 1989

Authors and Affiliations

  • A. C. M. Ran
    • 1
  • L. Roozemond
    • 2
  1. 1.Faculteit Wiskunde en InformaticaVrije UniversiteitAmsterdamThe Netherlands
  2. 2.Koninklijke/Shell Exploratie en Produktie LaboratoriumRijswijk ZHThe Netherlands

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