A characterization of the Schechter essential spectrum on Banach spaces and applications
The author characterizes the essential spectrum of a closed and densely defined linear operator \(A\) on a general Banach space \(X\) as the intersection of the spectra of \(A+K\), where \(K\) ranges either over all bounded linear operators such that \((\lambda-A)^{-1}K\in{\mathcal I}(X)\) for some \(\lambda\in\rho(A)\) or over all bounded linear operators such that \(K(\lambda-A)^{-1}\in{\mathcal I}(X)\) for some \(\lambda\in\rho(A)\). Here \(\rho(A)\) stands for the resolvent set of \(A\) and \({\mathcal I}(X)\) is an arbitrary two-sided ideal of the Banach algebra of bounded linear operators on \(X\) that is intermediate between that of the compact operators and that of the Fredholm perturbations. Some applications are given to the linear transport operator.
scientific article; zbMATH DE number 1836758
scientific article