Plus-operators in Krein spaces and dichotomous behavior of irreversible dynamical systems with discrete time

• Autores: V. Khatskevich, L. Zelenko
• Localización: Studia mathematica, ISSN 0039-3223, Vol. 177, Nº 3, 2006, págs. 195-210
• Idioma: inglés
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• Resumen

  • We study dichotomous behavior of solutions to a non-autonomous linear difference equation in a Hilbert space. The evolution operator of this equation is not continuously invertible and the corresponding unstable subspace is of infinite dimension in general. We formulate a condition ensuring the dichotomy in terms of a sequence of indefinite metrics in the Hilbert space. We also construct an example of a difference equation in which dichotomous behavior of solutions is not compatible with the signature of the indefinite metric.