Bands in Pervasive Pre-Riesz Spaces

Pre-Riesz spaces are partially ordered vector spaces which are order dense sub-spaces of vector lattices. A band in a pre-Riesz space can be extended to a band in the ambient vector lattice. The corresponding restriction property does not hold in general. We provide sucient conditions on the underlying space such that the restriction property for bands holds. As an application, we consider the space Lr(l10) of all regular operators on the space l10 of all nally constant sequences. We establish that Lr(l10) is pre-Riesz and that its subspace of all order continuous operators is a band in Lr(l10). Subject Classication (MSC2000): 46A40, 06F2