### R-Schauder decompositions. Some applications.

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We discuss a strong version of the Dunford-Pettis property, earlier named (DP*) property, which is shared by both ℓ₁ and ${\ell}_{\infty}$. It is equivalent to the Dunford-Pettis property plus the fact that every quotient map onto c₀ is completely continuous. Other weak sequential continuity results on polynomials and analytic mappings related to the (DP*) property are shown.

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