Assume that X is a (real) vector space, Y is an Archimedean vector lattice, and Z is a universally complete vector lattice. The operator equation 𝔛A=B, with A ∈ L(X,Y) and B ∈ L(X,Z), has a positive solution 𝔛 iff for all x ∈ X from Ax ≥0 it follows that Bx≥0. We discuss the status and validity of this claim within the relevant background of Boolean valued analysis.
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