Factorization of compact operators and finite representability of Banach spaces with applications to Schwartz spaces
Steven Bellenot (1978)
Studia Mathematica
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Steven Bellenot (1978)
Studia Mathematica
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P. Wojtaszczyk (1972)
Studia Mathematica
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M. Kadec (1971)
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. Pełczyński (1976)
Studia Mathematica
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A. A. Albanese, V. B. Moscatelli (1996)
Revista Matemática de la Universidad Complutense de Madrid
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We prove that the direct sum and the product of countably many copies of L[0, 1] are primary locally convex spaces. We also give some related results.
W. B. Johnson (1979-1980)
Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")
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V. Fonf, V. Shevchik (1999)
Studia Mathematica
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It is proved that a separable Banach space X admits a representation as a sum (not necessarily direct) of two infinite-codimensional closed subspaces and if and only if it admits a representation as a sum (not necessarily direct) of two infinite-codimensional operator ranges. Suppose that a separable Banach space X admits a representation as above. Then it admits a representation such that neither of the operator ranges , contains an infinite-dimensional closed subspace...
J. C. Díaz (1987)
Collectanea Mathematica
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Tadeusz Figiel (1972)
Mémoires de la Société Mathématique de France
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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.