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

TL;DR

This paper investigates the structure of certain operators on the order dual of an $f$-algebra, establishing conditions under which various classes of operators coincide.

Contribution

It proves that for $f$-algebras with the factorization property, orthomorphisms, $f$-orthomorphisms, and $f$-linear operators are equivalent.

Findings

Operators coincide under the factorization property

Characterization of $f$-orthomorphisms on the order dual

Unified view of operator classes in $f$-algebras

Abstract

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.