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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Godefroy, Gilles (2000)
Serdica Mathematical Journal
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We survey several applications of Simons’ inequality and state related open problems. We show that if a Banach space X has a strongly sub-differentiable norm, then every bounded weakly closed subset of X is an intersection of finite union of balls.
Frontisi, Julien (1996)
Serdica Mathematical Journal
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It is proved that a representable non-separable Banach space does not admit uniformly Gâteaux-smooth norms. This is true in particular for C(K) spaces where K is a separable non-metrizable Rosenthal compact space.
JESÚS A. JARAMILLO and ÁNGELES PRIETO M. ISABEL GARRIDO (2000)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
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M. Kadec (1971)
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...
W. Szlenk (1968)
Studia Mathematica
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Catherine Finet (1988)
Studia Mathematica
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Dick van Dulst, Ivan Singer (1976)
Studia Mathematica
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Wolfgang Lusky (1979)
Studia Mathematica
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