Almost Dunford–Pettis p-convergent operators

In this paper two classes of operators related to weakly p-compact and almost Dunford–Pettis sequences which will be called almost Dunford–Pettis p-convergent operators and weak almost p-convergent operators are studied. Some properties of Banach lattices, the weak Dunford–Pettis property of order p and the strong relatively compact Dunford–Pettis property of order p are characterized in terms of almost Dunford–Pettis p-convergent and weak almost p-convergent operators.