  The Riesz-Kantorovich formula expresses (under certain assumptions) the
supremum of two operators $S, T : X \to Y$ where $X$ and $Y$ are ordered linear
spaces as $$ S \vee T (x) = \sup_{0 \leqslant y \leqslant x} [S (y) + T (x -
y)]. $$ We explore some conditions that are sufficient for its validity, which
enables us to get extensions of known results characterizing lattice and
decomposition properties of certain spaces of order bounded linear operators
between $X$ and $Y$.
