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

• Autorzy: V. Khatskevich , L. Zelenko
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 39A10: Difference equations, additive
• 47B37: Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
• 37D99: None of the above, but in this section
• 47B50: Operators on spaces with an indefinite metric

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2006
• Tom: 177
• Numer: 3
• Strony: 195-210

Daty

wydano

2006

Twórcy

autor

V. Khatskevich

• Department of Mathematics, ORT Braude Academic College, P.O. Box 78, 21982 Karmiel, Israel

autor

L. Zelenko

• Department of Mathematics, University of Haifa, 31905 Haifa, Israel

Identyfikatory

DOI

10.4064/sm177-3-1