Band projections in spaces of regular operators

Abstract

We introduce inner band projections in the space of regular operators on a Dedekind complete Banach lattice and study some structural properties of this class. In particular, we provide a new characterization of atomic order continuous Banach lattices as those for which all band projections in the corresponding space of regular operators are inner. We also characterize the multiplication operators L A R B L_AR_B which are band projections precisely as those with A , B A,B being band projections up to a scalar multiple.