Equivalent norms on separable Asplund spaces
C. Finet, W. Schachermayer (1989)
Studia Mathematica
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C. Finet, W. Schachermayer (1989)
Studia Mathematica
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M. Kadec (1971)
Studia Mathematica
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V. Montesinos (1985)
Studia Mathematica
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G. Androulakis (1998)
Studia Mathematica
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Let (x_n) be a sequence in a Banach space X which does not converge in norm, and let E be an isomorphically precisely norming set for X such that (*) ∑_n |x*(x_{n+1} - x_n)| < ∞, ∀x* ∈ E. Then there exists a subsequence of (x_n) which spans an isomorphically polyhedral Banach space. It follows immediately from results of V. Fonf that the converse is also true: If Y is a separable isomorphically polyhedral Banach space then there exists a normalized M-basis (x_n) which spans Y and...
Patrick N. Dowling (2000)
Collectanea Mathematica
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We obtain refinement of a result of Partington on Banach spaces containing isomorphic copies of l-∞. Motivated by this result, we prove that Banach spaces containing asymptotically isometric copies of l-∞ must contain isometric copies of l-∞.
Catherine Finet (1988)
Studia Mathematica
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W. Szlenk (1968)
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W. Johnson, A. Szankowski (1976)
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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.
A. Pełczyński (1971)
Studia Mathematica
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P. Wojtaszczyk (1972)
Studia Mathematica
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