Order bounded local derivations on Archimedean almost f-algebras

Let A be an Archimedean almost integral-algebra and let d : A A be an order bounded local derivation. Then d is a generalized averaging operator on A, i.e., d (xd (y)) z = d (x) d (y)z for all x, y, z is an element of A. In the case where A is an Archimedeanf-algebra, the situation improves. Indeed, any order bounded local derivation on A is an averaging operator, i.e., d (xd (y)) = d (x) d (y) for all x, y is an element of A.