f-Orthomorphisms and f-Linear Operators on the Order Dual of an f-Algebra

In this paper we consider the $f$-orthomorphisms and $f$-linear operators on the order dual of an $f$-algebra. In particular, when the $f$-algebra has the factorization property (not necessarily unital), we prove that the orthomorphisms, $f$-orthomorphisms and $f$-linear operators on the order dual are precisely the same class of operators.