engleski

Nonuniform spectrum on Banach spaces

For a sequence of bounded linear operators acting on a Banach space, we consider the notion of nonuniform spectrum. This is defined in terms of the existence of nonuniform expo- nential dichotomies with an arbitrarily small nonuniform part and can be seen as a nonuniform version of the spectrum introduced by Sacker and Sell in the case of a single trajectory, al- though now in the infinite-dimensional setting. We will present complete characterization of all possible forms of the nonuniform spectrum for sequences of bounded linear operators satisfying a certain asymptotic compactness. Furthermore, we will discuss the relationship between nonuniform spectrum and the theory of Lyapunov exponents.

nonuniform spectrum, Lyapunov exponents

nije evidentirano