Some Properties of Unbounded M-Weakly and Unbounded L-Weakly Compact Operators

Abstract

We introduce the class of unbounded M-weakly compact operators and the class of unbounded L-weakly compact operators. We investigate some properties for this new classification of operators, and we study the relation between them and M-weakly compact and L-weakly compact operators. We also present an operator characterization of Banach lattices with an ordered continuous norm.