On the class of almost order Fredholm operators

In the current research paper, motivated by Fredholm theory, we introduce new classes of operators acting on Banach lattice spaces, called almost order semi-Fredholm. We elaborate some interesting properties of these classes. Additionally, some characterizations are expressed respectively in terms of almost order bounded sets and semi-compact operators. Finally, the basic relationships between almost order upper semi-Fredholm and upper semi-Fredholm operators are enacted.