Disjoint Dunford–Pettis-Type Properties in Banach Lattices

New characterizations of the disjoint Dunford–Pettis property of order p (disjoint DPPp) are proved and applied to show that a Banach lattice of cotype p has the disjoint DPPp whenever its dual has this property. The disjoint Dunford–Pettis^* property of order p (disjoint DP^*Pₚ) is thoroughly investigated. Close connections with the positive Schur property of order p, with the disjoint DPPp, with the p-weak DP^* property and with the positive DP^* property of order p are established. In a final section, we study the polynomial versions of the disjoint DPPp and of the disjoint DP^*Pₚ.