In operator theory characterizing extreme points has been systematically studied in a convex set of linear operators from an algebra to another. This paper presents some new characterizations. We define pre-Markov operators and identify when the second adjoint of a linear positive operator being an extreme point in the collection of all Markov operators between the unital second order duals of two unital f-algebras. Moreover a characterization of extreme points is given in the collection of all contractive operators between unital f-algebras. In addition, we give a condition that makes an order bounded algebra homomorphism is a lattice homomorphism.
Markov operator, f-algebra, algebra homomorphism, lattice homomorphism, contractive operator, Arens multiplication
DURU, HÜLYA and İLTER, SERKAN
Turkish Journal of Mathematics: Vol. 44:
6, Article 15.
Available at: https://journals.tubitak.gov.tr/math/vol44/iss6/15