Extreme contractive operators on Stone f-algebras

An Archimedean semiprime f-algebra A for which IA∧f∈Afor all  f∈A is called a Stone f-algebra, where IA is the identity operator on A. Moreover, an operator T between two Stone f-algebras A and B is said to be contractive if f∈Aand0≤f≤IAimply  0≤Tf≤IB. The set K(A,B) of all positive contractive operators from A into B is a convex set. This paper characterizes extreme points in K(A,B). In this regard, we prove that T∈K(A,B) is extreme if and only if T is an algebra homomorphism. Furthermore, we show that T∈K(A,B) is extreme if and only if T is a Stone operator, meaning that, T(IA∧f)=IB∧Tffor all  f∈A.