Some properties of the space of regular operators on atomic Banach lattices (Q545662)

Let \(L^{r}(E,X)\) denote the space of all regular linear operators from a Banach lattice \(E\) to a Banach lattice \(X\). In this paper among other things the authors show that if \(E\) is a separable atomic Banach lattice, then \(L^{r}(E,X)\) is reflexive if and only if both \(E\) and \(X\) are reflexive and each positive linear operator from \(E\) into \(X\) is compact.