Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Table of Contents - 1989 - Volume 111, Issue 3-4  

Research Article

Spectral properties of diagonally dominant infinite matrices, part I

F. O. Farida1 and P. Lancastera1

a1 Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada T2N 1N4

Synopsis

Theorems 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.

(Received March 23 1988)

(Revised July 26 1988)