On the surjective Dunford-Pettis property
We exhibit a general method to show that for several classes of Fréchet spaces the Three-space-problem fails. This method works for instance for the class of distinguished Fréchet spaces, for Fréchet spaces with the density condition and also for dual Fréchet spaces (which gives a negative answer to a question of D. Vogt). An example of a Banach space, which is not a dual Banach space but the strong dual of a DF-space, shows that there are two real different possibilities of defining the notion...
The main result in this paper is the following: Let E be a Fréchet space having a normable subspace X isomorphic to lp, 1 ≤ p < ∞, or to c0. Let F be a closed subspace of E. Then either F or E/F has a subspace isomorphic to X.
We describe the topological reflexive closure of the isometry group of the suspension of B(H).