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 𝐷𝑃∗𝑝
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 𝐷𝑃∗𝑝
property and the p-Dunford–Pettis sequentially compact property of order (𝑞′,𝑞)
in the class of all locally convex spaces.