Compact polynomials between Banach spaces.
Raquel Gonzalo, Jesús Angel Jaramillo (1993)
Extracta Mathematicae
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Raquel Gonzalo, Jesús Angel Jaramillo (1993)
Extracta Mathematicae
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Jesús M. Fernández Castillo, Ricardo García (2005)
Extracta Mathematicae
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Parviz Azimi, H. Khodabakhshian (2009)
Czechoslovak Mathematical Journal
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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...
Fetter, Helga, De Buen, Berta Gamboa (2010)
Fixed Point Theory and Applications [electronic only]
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Joaquín M. Gutiérrez, Jesús A. Jaramillo, José G. Llavona (1995)
Extracta Mathematicae
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In this paper we survey a large part of the results on polynomials on Banach spaces that have been obtained in recent years. We mainly look at how the polynomials behave in connection with certain geometric properties of the spaces.