Basic sequences and smooth norms in Banach spaces
Catherine Finet (1988)
Studia Mathematica
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Catherine Finet (1988)
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...
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 .
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.
C. Finet, W. Schachermayer (1989)
Studia Mathematica
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A. Pełczyński (1971)
Studia Mathematica
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Marek Wójtowicz (1997)
Collectanea Mathematica
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A simple way of obtaining separable quotients in the class of weakly countably determined (WCD) Banach spaces is presented. A large class of Banach lattices, possessing as a quotient c0, l1, l2, or a reflexive Banach space with an unconditional Schauder basis, is indicated.
V. Montesinos, J. R. Torregrosa (1991)
Collectanea Mathematica
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In this paper we prove that the geometrical notions of Rotundity and Uniform Rotundity of the norm in a Banach space are stable for the generalized Banach products.
T. Figiel (1972)
Studia Mathematica
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