Dunford-Pettis and Dieudonné polynomials on Banach spaces

Abstract

We introduce two classes of $m$-homogeneous polynomials defined on Banach spaces, which extend the classes of Dunford-Pettis and Dieudonné linear operators. These extensions allow us to prove that several characterization theorems related to the Dunford-Pettis, Schur, and reciprocal Dunford-Pettis properties, are also valid in the more general case of homogeneous polynomials of any degree $m\in\N$.