Positive operators on riesz spaces

This thesis consisted of five parts. The first part was about introduction. In the second part, vector space, ordered vector space, Banach space and some basic concepts about operators in Riesz space were given. In the third part, Riesz space concept was examined in detail. Some important definitions and theorems related to positive operators in Riesz space were explained. Additionally, Dedekind complete Riesz space and Archimedean Riesz space were mentioned, and information about conclusions of them were examined in detail. In the fourth part, concepts of band preserving operators and orthomorphisms were discussed after f-algebras and their properties. Relationships between f-algebras and orthomorphism were given. Moreover, central operators, which is subset of orthomorphism, and conjugate of central operators were stated. In the fifth and last part, conclusions were interpreted.