We consider the -orthomorphisms and -linear operators on the order dual of an -algebra. In particular, when the -algebra has the factorization property (not necessarily unital), we prove that the orthomorphisms, -orthomorphisms, and -linear operators on the order dual are precisely the same class of operators.
"-Orthomorphisms and -Linear Operators on the Order Dual of an -Algebra." Abstr. Appl. Anal. 2012 1 - 7, 2012. https://doi.org/10.1155/2012/971560