Almost L-dunford-pettis Property In Banach Lattices And Their Related Operators

L-Dunford-Pettis property and b-limited operators have strong application and development in Banach lattices.By the definition of L-Dunford-Pettis property and b-limited operators,we mainly give the notion of almost L-Dunford-Pettis property and b-almost Dunford-Pettis operators in Banach lattices,which related properties are investigated.Firstly,the definition of the almost L-Dunford-Pettis property is introduced.We give a characterization of the almost L-Dunford-Pettis property with respect to some properties of Banach lattices and operators(disjoint Dunford-Pettis completely continuous operators,weak compact operators).It thinks over the connection between almost L-Dunford-Pettis property and weak Dunford-Pettis property.We study the definition of almost L-Dunford-Pettis operators and its basic property.Secondly,it introduces the notion of b-almost Dunford-Pettis operators,which some properties are discussed.We investigate the relationship between b-almost Dunford-Pettis operators and other operators(b-weak compact operator,weak compact operators,almost Dunford-Pettis operators).