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 (1992)
Extracta Mathematicae
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Çalişkan, Erhan (2004)
Portugaliae Mathematica. Nova Série
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Jesús A. Jaramillo, Angeles Prieto Yerro (1991)
Extracta Mathematicae
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We shall be concerned in this note with some questions posed by Carne, Cole and Gamelin in [3], involving the weak-polynomial convergence and its relation to the tightness of certain algebras of analytic functions on a Banach space.
Rajappa K. Asthagiri (1991)
Extracta Mathematicae
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In this paper it is shown that the class L (E,E,...,E;F) of weakly uniformly continuous n-linear mappings from Ex Ex...x E to F on bounded sets coincides with the class L (E,E,...,E;F) of weakly sequentially continuous n-linear mappings if and only if for every Banach space F, each Banach space E for i = 1,2,...,n does not contain a copy of l.
Jesús M. Fernández Castillo, Manuel González (1991)
Extracta Mathematicae
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In 1930, J. Schreier [10] introduced the notion of admissibility in order to show that the now called weak-Banach-Saks property does not hold in every Banach space. A variation of this idea produced the Schreier's space (see [1],[2]). This is the space obtained by completion of the space of finite sequences with respect to the following norm: ||x||S = sup(A admissible) ∑j ∈ A |xj|, ...
Jesús M. Fernández Castillo, Ricardo García (2005)
Extracta Mathematicae
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Manuel González, Joaquín M. Gutiérrez (1991)
Extracta Mathematicae
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We introduce and characterize the class P of polynomials between Banach spaces whose restrictions to Dunford-Pettis (DP) sets are weakly continuous. All the weakly compact and the scalar valued polynomials belong to P. We prove that a Banach space E has the Dunford-Pettis (DP) property if and only if every P ∈ P is weakly sequentially continuous. This result contains a characterization of the DP property given in [3], answering a question of Pelczynski: E has the DP property if and only...
Manuel González, Joaqín Gutiérrez (1996)
Studia Mathematica
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We prove a basic property of continuous multilinear mappings between topological vector spaces, from which we derive an easy proof of the fact that a multilinear mapping (and a polynomial) between topological vector spaces is weakly continuous on weakly bounded sets if and only if it is weakly uniformly} continuous on weakly bounded sets. This result was obtained in 1983 by Aron, Hervés and Valdivia for polynomials between Banach spaces, and it also holds if the weak topology is replaced...
Fernando Bombal, Pilar Cembranos, José Mendoza (1989)
Extracta Mathematicae
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