Abstract
Let H be a not necessarily separable Hilbert space, and let BH denote the space of all bounded linear operators on H. It is proved that a commutative lattice D of self-adjoint projections in H that contains 0 and I is spatially complete if and only if it is a closed subset of BH in the strong operator topology. Some related results are obtained concerning commutative lattice-ordered cones of self-adjoint operators that contain D. 2000 Mathematics Subject Classification 47D03, 47L35, 47L07, 46L10, 54F05, 54G05, 46E05.
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