Unbounded L-weakly compact operators and a generalization of M-weakly compact operators

In this paper, we present and examine novel classifications of operators called unbounded L-weakly compact operators and generalized M-weakly compact operators. We explore various lattice properties associated with these operator classifications and investigate their connections with other well-known operators, including M-weakly compact operators. Our findings reveal that every M-weakly compact operator is a generalized M-weakly compact operator, although the converse does not hold in general. We also investigate the duality properties of this class of operators.