Banach spaces in which all multilinear forms are weakly sequentially continuous
Jesús Castillo, Ricardo García, Raquel Gonzalo (1999)
Studia Mathematica
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We solve several problems in the theory of polynomials in Banach spaces. (i) There exist Banach spaces without the Dunford-Pettis property and without upper p-estimates in which all multilinear forms are weakly sequentially continuous: some Lorentz sequence spaces, their natural preduals and, most notably, the dual of Schreier's space. (ii) There exist Banach spaces X without the Dunford-Pettis property such that all multilinear forms on X and X* are weakly sequentially continuous; this...