Abstract: We introduce new concept of almost demi Dunford-Pettis operators. Let E be a Banach lattice. An operator T from E into E is said to be almost demi Dunford-Pettis if, for every sequence \{x_{n}\} in E_{+} such that x_{n}\rightarrow 0 in \sigma(E,E') and \|x_{n}-Tx_{n}\|\rightarrow 0 as n\rightarrow \infty, we have \|x_{n}\|\rightarrow 0 as n\rightarrow \infty. In addition, we study some properties of this class of operators and its relationships with others known operators.
Keywords: almost demi Dunford-Pettis operator; Banach lattice; positive Schur property
DOI: DOI 10.14712/1213-7243.2024.007
AMS Subject Classification: 46A40 46B40 46B42