Asymptotic similarity of infinite-dimensional linear systems and applications to stability (Q2721947)

The notion of similarity for linear systems is extended to the infinite-dimensional setting. Wheras the similarity operator is assumed to be bounded with bounded inverse this assumption is too restrictive in the infinite-dimensional setting. The author introduces a generalization called asymptotic similarity which in the finite-dimensional case reduces to the well-known similarity notion. Asymptotic similarity preserves the spectrum and the exponential growth rates.