Holomorphic functions on Fréchet spaces with Schauder basis.
Seán Dineen (1995)
Extracta Mathematicae
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Seán Dineen (1995)
Extracta Mathematicae
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Jorge Mújica (1997)
Revista Matemática de la Universidad Complutense de Madrid
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In this survey we show that the separable quotient problem for Banach spaces is equivalent to several other problems for Banach space theory. We give also several partial solutions to the problem.
Jorge Mujica (1997)
Studia Mathematica
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We show that if U is a balanced open subset of a separable Banach space with the bounded approximation property, then the space ℋ(U) of all holomorphic functions on U, with the Nachbin compact-ported topology, is always bornological.
Vincenzo Moscatelli (1990)
Studia Mathematica
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A. Pełczyński (1971)
Studia Mathematica
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J. Lindenstrauss, A. Pełczyński (1968)
Studia Mathematica
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William Johnson (1974)
Studia Mathematica
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Ginés López (1999)
Studia Mathematica
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We prove that a Banach space X with a supershrinking basis (a special type of shrinking basis) without copies is somewhat reflexive (every infinite-dimensional subspace contains an infinite-dimensional reflexive subspace). Furthermore, applying the -theorem by Rosenthal, it is proved that X contains order-one quasireflexive subspaces if X is not reflexive. Also, we obtain a characterization of the usual basis in .
Juan Carlos Díaz Alcaide (1993)
Publicacions Matemàtiques
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The main result in this paper is the following: Let E be a Fréchet space having a normable subspace X isomorphic to l, 1 ≤ p < ∞, or to c. Let F be a closed subspace of E. Then either F or E/F has a subspace isomorphic to X.
A. Pełczyński (1960)
Studia Mathematica
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P. Wojtaszczyk (1973)
Studia Mathematica
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