Spectral properties of diagonally dominant infinite matrices, part I

Abstract

SynopsisTheorems of Gersgorin-type are established for a diagonally dominant, unbounded, infinite matrix operator A acting on lp for some l ≦p≦∞. The results are established using an approximating sequence of infinite matrices An that converges to A in the generalised sense as n → ∞. This constructive approach admits approximation of the spectral properties of A by those of An.