c, l and l in function spaces.
Pilar Cembranos (1997)
Extracta Mathematicae
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Displaying similar documents to “Complemented copies of c0 in vector-valued Köthe-Dieudonné function spaces.”
c, l and l in function spaces.
Fréchet spaces of continuous vector-valued functions: Complementability in dual Fréchet spaces and injectivity
P. Domański, L. Drewnowski (1992)
Studia Mathematica
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Fréchet spaces of strongly, weakly and weak*-continuous Fréchet space valued functions are considered. Complete solutions are given to the problems of their injectivity or embeddability as complemented subspaces in dual Fréchet spaces.
Fréchet-spaces-valued measures and the AL-property.
S. Okada, W. J. Ricker (2003)
RACSAM
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Associated with every vector measure m taking its values in a Fréchet space X is the space L(m) of all m-integrable functions. It turns out that L(m) is always a Fréchet lattice. We show that possession of the AL-property for the lattice L(m) has some remarkable consequences for both the underlying Fréchet space X and the integration operator f → ∫ f dm.
On the three-space property: non-containment of l, 1 ≤ p < ∞, or c subspaces.
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.
Complemented copies of c in C(Ω).
Juan Carlos Ferrando, Manuel López Pellicer (2001)
RACSAM
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En esta nota consideramos una clase de espacios topológicos de Hausdorff localmente compactos (Ω) con la propiedad de que el espacio de Banach C(Ω) de todas las funciones continuas con valores escalares definidas en Ω que se anulan en el infinito, equipado con la norma supremo, contiene una copia de C norma-uno complementada, mientras que C (βΩ) contiene una copia de l linealmente isométrica.
Quasinormable X-Kothe Echelon spaces.
FERNANDO BLASCO (2000)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
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On non-primary Fréchet Schwartz spaces
J. Díaz (1997)
Studia Mathematica
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Let E be a Fréchet Schwartz space with a continuous norm and with a finite-dimensional decomposition, and let F be any infinite-dimensional subspace of E. It is proved that E can be written as G ⨁ H where G and H do not contain any subspace isomorphic to F. In particular, E is not primary. If the subspace F is not normable then the statement holds for other quasinormable Fréchet spaces, e.g., if E is a quasinormable and locally normable Köthe sequence space, or if E is a space of holomorphic...
Sobczyk's theorems from A to B.
Félix Cabello Sánchez, Jesús M. Fernández Castillo, David Yost (2000)
Extracta Mathematicae
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Sobczyk's theorem is usually stated as: . Nevertheless, our understanding is not complete until we also recall: . Now the limits of the phenomenon are set: although c is complemented in separable superspaces, it is not necessarily complemented in a non-separable superspace, such as l.
On the three-space problem and the lifting of bounded sets.
Susanne Dierolf (1993)
Collectanea Mathematica
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We exhibit a general method to show that for several classes of Fréchet spaces the Three-space-problem fails. This method works for instance for the class of distinguished Fréchet spaces, for Fréchet spaces with the density condition and also for dual Fréchet spaces (which gives a negative answer to a question of D. Vogt). An example of a Banach space, which is not a dual Banach space but the strong dual of a DF-space, shows that there are two real different possibilities of defining...
The problem of complementability for some spaces of vector measures of bounded variation with values in Banach spaces containing copies of
L. Drewnowski, G. Emmanuele (1993)
Studia Mathematica
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Let (S, ∑, m) be any atomless finite measure space, and X any Banach space containing a copy of . Then the Bochner space is uncomplemented in ccabv(∑,m;X), the Banach space of all m-continuous vector measures that are of bounded variation and have a relatively compact range; and ccabv(∑,m;X) is uncomplemented in cabv(∑,m;X). It is conjectured that this should generalize to all Banach spaces X without the Radon-Nikodym property.