Strongly alternative Dunford - Pettis subspaces of operator ideals - Moshtaghioun, S. M. (Ukrains’kyi Matematychnyi Zhurnal, 2013)
Introducing the concept of strong alternative Dunford – Pettis property (strong DP1) for the subspace M of operator ideals U(X, Y ) between Banach spaces X and Y, we show that M is a strong DP1 subspace if and only if all evaluation operators φ_x : M → Y та ψy∗ : M → X^* are DP1 operators, where φ_x(T) = T x та ψ_y^∗ (T) = T^∗y^∗ for x ∈ X, y^∗ ∈ Y and T ∈ M. Some consequences related to the concept of alternative Dunford – Pettis property in subspaces of some operator ideals are obtained.