Statistical Dunford-Pettis operators on Banach Spaces

Abstract

We introduce the concept of statistical Dunford-Pettis operators in this paper, which extend the classical notion of Dunford-Pettis operators into the domain of statistical convergence. These operators are defined on Banach spaces by their ability to map sequences that converge weakly in a statistical sense into sequences that converge statistically. The exploration includes the properties of these operators and their connections to other operator classes, such as statistically continuous and statistically compact operators. Furthermore, we examine the behavior of the adjoint operators associated with the statistical Dunford-Pettis operators.