On theorems of de Pagter and Ando-Krieger (Q1085418)

Let T be a positive, compact operator in a Banach lattice E (dim \(E\geq 2)\) and let T be band irreducible. Obviously this condition is less restrictive than that of ideal-irreducibility. The author proves that in the above reviewed de Pagtes's theorem one can assume T to be only band- irreducible but demanding instead that T be order \(\sigma\)-continuous.