Properties of ideal and band operators defined between Riesz spaces

Let G and H be Riesz spaces, T:G→H be an operator. T is called ideal operator if T(I) is an ideal in H for each ideal I in G; similarly, it is called band operator if T(B) is a band in H for each band B in G. In this thesis, the properties of ideal and band operators defined between Riesz spaces, comparisons between each other as well as with disjointness preserving operators, conditions of being order bounded and their properties when they are order bounded are studied. The conditions in which the invertible ideal and band operators' inverse provide the same properties are researched. Furthermore, solutions of the two problems concerning the theory of disjointness preserving operators are offered and the properties of the band operators are investigated by extending the definition of band operator to pre-Riesz spaces.