A closed range theorem for the Frobenius-Perron operator and its application to the spectral analysis
The theory of functional analysis is used to obtain some new general results of Frobenius-Perron operators \(P_ S: L^ 1(X)\to L^ 1(X)\) and Koopman operators \(U_ S: L^ \infty(X)\to L^ \infty(X)\). As an application of these results, new necessary and sufficient conditions are got for \(P_ S\) and \(U_ S\) to be isometric, respectively, and so in this case the spectrum of \(P_ S\) is completely determined.
scientific article; zbMATH DE number 617449