Statistically order compact operators on Riesz spaces

This research paper introduces and establishes the concept of compact operators in the context of Riesz spaces, specifically considering statistical order convergence. We define statistical order compact operators as operators that map statistical order bounded sequences to sequences with statistical order convergent subsequences. Additionally, we define statistical $M$-weakly compact operators. By utilizing these non-topological concepts, we derive some new results pertaining to these operators.