The uniform boundedness principle for order bounded operators
It is shown that for a sequence of order bounded linear operators from a Dedekind \(\sigma\)-complete vector lattice to a Dedekind complete vector lattice with an order unit which is order bounded pointwise is uniformly order bounded on order bounded subsets. By an example it is shown that the result does not hold if the vector lattices are assumed to be Dedekind complete, but there is no order unit in the image space.
sequence of order bounded linear operators from a Dedekind \(\sigma\)- complete vector lattice to a Dedekind complete vector lattice with an order unit
uniformly order bounded on order bounded subsets
scientific article; zbMATH DE number 4131007