Examination of some special operators and operator semigroups defined on riesz spaces

The study of operator classes in lattice theory holds great importance. The analysis of operators based on order convergence and norm convergence has made significant contributions to operator theory. Additionally, some of these operator classes assist in examining the properties satisfied by the $C_0$-semigroup and its generator. Moreover, in recent years, the demi versions of certain operators have attracted attention, and studies have been conducted on their properties. In this thesis, quasi Levi operators based on order convergence and quasi KB operators based on norm convergence have been examined.\\ Furthermore, the definitions of the demi versions of these operators have been given, and their properties have been investigated. Additionally, the behavior of the generator has been examined in the case where some of the operators constituting the $C_0$-semigroup are demi quasi-KB operators.