2018/05/09 by Duru, Hülya, Ilter, Serkan
#46B42 #46H25 #47B38 #47B60 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.1805.03646
A positive linear operator T between two unital f-algebras, with point separating order duals, A and B is called a Markov operator for which % T( e1) =e2 where e1,e2 are the identities of A and B respectively. Let A and B be semiprime f-algebras with point separating order duals such that their second order duals A∼ ∼ and B∼ ∼ are unital f-algebras. In this case, we will call a positive linear operator T:A→ B to be a Pre-Markov operator, if the second adjoint operator of T is a Markov operator. A positive linear operator T between two semiprime f-algebras, with point separating order duals, A and B is said to be contractive if Ta∈ B∩ [ 0,IB] whenever a∈ A∩ [ 0,IA] , where IA and IB are the identity operators on A and B respectively. In this paper we characterize pre-Markov algebra homomorphisms. In this regard, we show that a pre-Markov operator is an algebra homomorphism if and only if its second adjoint operator is an extreme point in the collection of all Markov operators from A∼ ∼ to B∼ ∼ . Moreover we characterize extreme points of contractive mappings from A to B. In addition, we give a condition that makes an order bounded algebra homomorphism is a lattice homomorphism.