A generalization of M-weakly compact operators

In this paper, we introduce and study new classifications of operators as name unbounded L-weakly and generalized M-weakly compact operators. We study some lattice properties of these classifications of operators and we investigate their relationships with others known operators such as M-weakly compact operators. We show that each M-weakly compact operator is generalized M-weakly compact operator, but the converse, in general, not holds. Mathematics Subject Classification (2010) 47B65 · 46B40 · 46B42