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On strong α-stability of invariant subspaces of matrices

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The Gohberg Anniversary Collection

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 40/41))

Abstract

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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References

  1. Bart, H., Gohberg, I. and Kaashoek, M. A.: Minimal Factorization of Matrix and Operator Functions, Birkhäuser, Basel, 1979.

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  2. Campbell, S. and Daughtry, J.: The stable solutions of quadratic matrix equations, Proc. AMS 74 (1979), 19–23.

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  3. Gohberg, I., Lancaster, P. and Rodman, L.: Invariant Subspaces of Matrices with Applications, John Wiley & Sons, New York, 1986.

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  4. 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.

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Author information

Authors and Affiliations

  1. Faculteit Wiskunde en Informatica, Vrije Universiteit, De Boelelaan 1081, 1081 HV, Amsterdam, The Netherlands

    A. C. M. Ran

  2. Koninklijke/Shell Exploratie en Produktie Laboratorium, P.O.Box 60, 2280 AB, Rijswijk ZH, The Netherlands

    L. Roozemond

Authors
  1. A. C. M. Ran
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  2. L. Roozemond
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Computer Science, Vrije Universiteit, Amsterdam, The Netherlands

    H. Dym , S. Goldberg , M. A. Kaashoek  & P. Lancaster , ,  & 

Additional information

Dedicated to professor I. Gohberg on the occasion of his sixtieth birthday

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© 1989 Birkhäuser Verlag Basel

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Ran, A.C.M., Roozemond, L. (1989). On strong α-stability of invariant subspaces of matrices. In: Dym, H., Goldberg, S., Kaashoek, M.A., Lancaster, P. (eds) The Gohberg Anniversary Collection. Operator Theory: Advances and Applications, vol 40/41. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-9144-8_14

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  • DOI: https://doi.org/10.1007/978-3-0348-9144-8_14

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9924-6

  • Online ISBN: 978-3-0348-9144-8

  • eBook Packages: Springer Book Archive

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