On the class of demi-U-Dunford-Pettis operators

Abstract

Our main objective in this paper is to introduce and study a new class of operators named demi-U-Dunford-Pettis. This class is positioned between the class of demi Dunford-Pettis operators and order weakly demicompact operators, and it contains the class of U-Dunford-Pettis operators. Specifically, we characterize the Banach lattices on which all operators are demi-U-Dunford-Pettis and examine its connections with other classes of operators. Additionally, we investigate results concerning the sum of two operators, the product of two operators, the power of operators, the domination property and operator n×n matrix of this class. Furthermore, we characterize Banach lattices for which each demi U-Dunford-Pettis operator is b-weakly demicompact (resp. demi Dunford-Pettis) and each order weakly demicompact operator (resp. b-weakly demicompact) is demi-U-Dunford-Pettis.