Displaying similar documents to “Compact polynomials between Banach spaces.”

Polynomials and geometry of Banach spaces.

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.

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...

Polynomial characterizations of Banach spaces not containing l.

Joaquín M. Gutiérrez (1991)

Extracta Mathematicae

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Many properties of Banach spaces can be given in terms of (linear bounded) operators. It is natural to ask if they can also be formulated in terms of polynomial, holomorphic and continuous mappings. In this note we deal with Banach spaces not containing an isomorphic copy of l, the space of absolutely summable sequences of scalars.

An approach to Schreier's space.

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|, ...

Remarks on the weak-polynomial convergence on a Banach space.

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.

Polynomial characterizations of the Dunford-Pettis property.

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...