Drop property equals reflexivity
V. Montesinos (1987)
Studia Mathematica
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V. Montesinos (1987)
Studia Mathematica
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S. Rolewicz (1987)
Studia Mathematica
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Jesús M. Fernández Castillo (1992)
Extracta Mathematicae
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Whitfield, J. H. M.
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Alistair Bird, Niels Jakob Laustsen (2010)
Banach Center Publications
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We create a new family of Banach spaces, the James-Schreier spaces, by amalgamating two important classical Banach spaces: James' quasi-reflexive Banach space on the one hand and Schreier's Banach space giving a counterexample to the Banach-Saks property on the other. We then investigate the properties of these James-Schreier spaces, paying particular attention to how key properties of their 'ancestors' (that is, the James space and the Schreier space) are expressed in them. Our main...
D. P. Sinha, K. K. Arora (1997)
Collectanea Mathematica
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Ehrhard Behrends, Michael Cambern (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...
J. Ayerbe, T. Domínguez Benavides, S. Cutillas (1997)
Colloquium Mathematicae
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We define a modulus for the property (β) of Rolewicz and study some useful properties in fixed point theory for nonexpansive mappings. Moreover, we calculate this modulus in spaces for the main measures of noncompactness.