Spectral continuity relative to invariant subspaces
Let \(E\) be a closed subspace of a Banach space \(X\). For the set of all linear operators on \(X\) for which \(E\) is invariant, the authors investigate convergence of the spectra and some of their standard subsets in the case of convergence of the sequence of operators. Similar problems are solved for restrictions of these operators on \(E\) and for induced operators on \(X/E\).
scientific article; zbMATH DE number 6706379