Algebraic operators on Riesz Spaces

This study, in which algebraic and locally algebraic order bounded disjointness preserving operators on vector lattices are investigated, contains three chapters. In the first chapter, the literature concerning the theory of positive operators is shortly given and the aim of this study is stated. In the second chapter, starting from the elementary ones, definitions and theorems which are mentioned in the study are given. In the third chapter which includes the main part of study, it is proven that strongly diagonal operators and algebraic orthomorphisms on an Archimedean vector lattice L coincide. The minimal polynomial T  of an algebraic orthomorphism T on L is described. Properties of vector lattices on which algebraic and locally algebraic orthomorphisms coincide are investigated. A necessary and sufficient condition is given for locally algebraic orthomorphisms on L to be strongly diagonal. Properties of algebraic order bounded disjointness preserving operators are investigated in connection with strongly diagonal operators. ix Key Words: Vector lattice, orthomorphism, minimal polynomial, algebraic operator, order bounded operator, disjointness preserving operator, strongly diagonal operator.