Locally Convex Spaces with Sequential Dunford–Pettis Type Properties

Let p,q,q′∈[1,∞], q′≤q. Several new characterizations of locally convex spaces with the sequential Dunford–Pettis property of order (p,q) are given. We introduce and thoroughly study the sequential Dunford–Pettis* property of order (p,q) of locally convex spaces (in the realm of Banach spaces, the sequential DP(p,∞)* property coincides with the well-known DPp* property). Being motivated by the coarse p-DP* property and the p-Dunford–Pettis relatively compact property for Banach spaces, we define and study the coarse sequential DP(p,q)* property, the coarse DPp* property and the p-Dunford–Pettis sequentially compact property of order (q′,q) in the class of all locally convex spaces.