Abstract
In this paper we consider various stability properties of real invariant lagrangian subspaces for real matrices which are either symmetric or skew-symmetric in a real quadratic form which may be symmetric or skew-symmetric itself. In particular, apart from ordinary stability we shall consider strong stability, which seems to be more desirable from a numerical point of view. For the classes of matrices we consider here stable subspaces are not always strongly stable, in contrast with the previous work. We shall completely characterize strongly stable invariant lagrangian subspaces, and in many cases also the stable ones. Invariant lagrangian subspaces with other stability properties, such as Lipschitz stability, are characterized as well.
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References
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Dedicated to Professor Israel Gohberg on the occasion of his sixtieth birthday.
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© 1989 Birkhäuser Verlag Basel
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Ran, A.C.M., Rodman, L. (1989). Stability of Invariant Lagrangian Subspaces II. In: Dym, H., Goldberg, S., Kaashoek, M.A., Lancaster, P. (eds) The Gohberg Anniversary Collection. Operator Theory: Advances and Applications, vol 40. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9276-6_15
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DOI: https://doi.org/10.1007/978-3-0348-9276-6_15
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-9974-1
Online ISBN: 978-3-0348-9276-6
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