Pre-Markov operators

DURU H., İLTER S.

TURKISH JOURNAL OF MATHEMATICS, vol.44, no.6, pp.2166-2173, 2020 (SCI-Expanded, Scopus, TRDizin) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 44 Issue: 6
  • Publication Date: 2020
  • Doi Number: 10.3906/mat-1910-59
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.2166-2173
  • Istanbul University Affiliated: Yes

Abstract

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.