Plus-operators in Krein spaces and dichotomous behavior of irreversible dynamical systems with discrete time
Tom 177 / 2006
Studia Mathematica 177 (2006), 195-210
MSC: Primary 47B50, 37D99; Secondary 39A10, 47B37.
DOI: 10.4064/sm177-3-1
Streszczenie
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.
