2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65192Andreu et al [2] and Sadovskii [11] used representation spaces to study measures of non-compactness and spectral radii of operators on Banach lattices. In this paper, we develop representation spaces based on the nonstandard hull construction (which is equivalent to the ultrapower construction). As a particular application, we present a simple proof and some extensions of the main result of de Pagter and Schep [6] on the monotonicity of the measure of non-compactness and the spectral radius of AM-compact operators. We also use the representation spaces to characterize d-convergence and discuss the relationship between d-convergence and the measures of non-compactness.To appear in PositivityFunctional Analysis47B06, 47B60, 47B65, 47A10, 47B10, 46B08, 46B42, 46B50, 26E35, 46S20text