Displaying similar documents to “Factorization of weakly continuous holomorphic mappings”

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.

Weak uniform continuity and weak sequential continuity of continuous n-linear mappings between Banach spaces.

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.

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...

On multilinear mappings attaining their norms.

Maria Acosta (1998)

Studia Mathematica

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We show, for any Banach spaces X and Y, the denseness of the set of bilinear forms on X × Y whose third Arens transpose attains its norm. We also prove the denseness of the set of norm attaining multilinear mappings in the class of multilinear mappings which are weakly continuous on bounded sets, under some additional assumptions on the Banach spaces, and give several examples of classical spaces satisfying these hypotheses.

Surjective factorization of holomorphic mappings

Manuel Gonzalez, Joaquín M. Gutiérrez (2000)

Commentationes Mathematicae Universitatis Carolinae

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We characterize the holomorphic mappings f between complex Banach spaces that may be written in the form f = T ∘ g , where g is another holomorphic mapping and T belongs to a closed surjective operator ideal.

Compact homomorphisms between algebras of analytic functions

Richard Aron, Pablo Galindo, Mikael Lindström (1997)

Studia Mathematica

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We prove that every weakly compact multiplicative linear continuous map from H ∞ ( D ) into H ∞ ( D ) is compact. We also give an example which shows that this is not generally true for uniform algebras. Finally, we characterize the spectra of compact composition operators acting on the uniform algebra H ∞ ( B E ) , where B E is the open unit ball of an infinite-dimensional Banach space E.