Generalized asymptotic constants
Let \(U_ t=\exp (-iHt)\) be an evolution in the Hilbert space \({\mathcal H}\). A bounded operator X in \({\mathcal H}\) is said to be a smooth asymptotic constant if on some set of vectors in \({\mathcal H}\quad \quad U_{-t}XU_ t\) converges very rapidly as \(t\to \infty\) [see, for details, \textit{M. Wollenberg}, Math. Nachr. 126, 217-229 (1986; Zbl 0609.47017)]. In some applications (e.g. scattering theory) interesting cases appear in which X is not bounded. In the paper under review an abstract notion of generalised asymptotic constant (X unbounded) is introduced and some of its elementary properties are investigated.
scientific article; zbMATH DE number 4071698