Copyright © 2012 Ying Feng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.