An absolute continuity for positive operators on Banach lattices

Abstract

For positive operators on a Banach lattice, absolute contnuity conditions are considered. An operator absolutely continuous with respect to T is compared to sums of compositions of T together with orthomorphisms or in special cases projections. Consequences For compact operators on functions spaces C(X) are considered.

Keywords

• Banach lattices
• orthomorphisms
• quasi- interior points.