Components of positive operators (Q917885)

Let X be a Dedekind complete Riesz space, and A be a subset of the Boolean algebra \({\mathcal B}(X)\) of all bands in X. The author presents some criteria for A to generate the whole set \({\mathcal B}(X)\). These results can be considered as a generalization of the corresponding results due to Ben de Pagter and C. D. Aliprantis and O. Burkinshaw. The technique of nonstandard analysis is used.