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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.
David Yost (1997)
Extracta Mathematicae
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Marián Fabian, Gilles Godefroy (1988)
Studia Mathematica
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M. Ostrovskiĭ (1993)
Studia Mathematica
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The main result: the dual of separable Banach space X contains a total subspace which is not norming over any infinite-dimensional subspace of X if and only if X has a nonquasireflexive quotient space with a strictly singular quotient mapping.
A. González, Vicente Montesinos (2009)
Czechoslovak Mathematical Journal
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We prove that weakly Lindelöf determined Banach spaces are characterized by the existence of a ``full'' projectional generator. Some other results pertaining to this class of Banach spaces are given.
L. Vašák (1981)
Studia Mathematica
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Manuel Valdivia (1997)
Revista Matemática de la Universidad Complutense de Madrid
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Jesús Ferrer, Marek Wójtowicz (2011)
Open Mathematics
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Let X, Y be two Banach spaces. We say that Y is a quasi-quotient of X if there is a continuous operator R: X → Y such that its range, R(X), is dense in Y. Let X be a nonseparable Banach space, and let U, W be closed subspaces of X and Y, respectively. We prove that if X has the Controlled Separable Projection Property (CSPP) (this is a weaker notion than the WCG property) and Y is a quasi-quotient of X, then the structure of Y resembles the structure of a separable Banach space: (a)...