Spectrum localizations for matrix operators on lp spaces

摘要

We investigate localization of spectra of infinite matrices that can act as linear operators from the Banach space lp,1≤p≤∞, to itself. To that end, we propose a method that is based on generalization of a strict diagonal dominance of infinite matrices that is adapted to lp and lq norms. Results are illustrated with several examples, and some interesting applications are discussed.