The order properties of \(r\)-compact operators on Banach lattices (Q884918)

Let \(\mathcal F(E,F)\) stand for the \(r\)-closure of finite-rank operators from \(E\) to \(F\), with \(E\) and \(F\) Banach lattices. The authors prove that \(\mathcal F(E,F)\) is a generalized sublattice of \({\mathcal L}^{r}(E,F)\). A few relevant properties are also demonstrated.