Semi-compactness of Null almost L-weakly and Null almost M-weakly compact operators

In this paper, we investigate Banach lattices on which each positive semi-compact operator \(T: E\rightarrow F\) $T:E\to F$ is null almost L-weakly compact (rep. Null almost M-weakly compact). Additionally, we present certain sufficient and necessary conditions for a positive Null almost L-weakly compact operator to be semi-compact.