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 LARB which are band projections precisely as those with A,B being band projections up to a scalar multiple.
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