A stronger Dunford–Pettis property
Tom 184 / 2008
Studia Mathematica 184 (2008), 205-216 MSC: Primary 46B20; Secondary 46G20. DOI: 10.4064/sm184-3-1
We discuss a strong version of the Dunford–Pettis property, earlier named $(DP^*)$ property, which is shared by both $\ell _1$ and $\ell _\infty .$ It is equivalent to the Dunford–Pettis property plus the fact that every quotient map onto $c_0$ is completely continuous. Other weak sequential continuity results on polynomials and analytic mappings related to the $(DP^*)$ property are shown.