Asplund spaces for beginners
David Yost (1993)
Acta Universitatis Carolinae. Mathematica et Physica
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David Yost (1993)
Acta Universitatis Carolinae. Mathematica et Physica
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L. Vašák (1981)
Studia Mathematica
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Marián Fabian, Gilles Godefroy (1988)
Studia Mathematica
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David Yost (1997)
Extracta Mathematicae
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C. S. Barroso, M. A. M. Marrocos, M. P. Rebouças (2013)
Studia Mathematica
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We establish some results that concern the Cauchy-Peano problem in Banach spaces. We first prove that a Banach space contains a nontrivial separable quotient iff its dual admits a weak*-transfinite Schauder frame. We then use this to recover some previous results on quotient spaces. In particular, by applying a recent result of Hájek-Johanis, we find a new perspective for proving the failure of the weak form of Peano's theorem in general Banach spaces. Next, we study a kind of algebraic...
Whitfield, J. H. M.
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J. Orihuela, W. Schachermayer, M. Valdivia (1991)
Studia Mathematica
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I. Singer (1961)
Studia Mathematica
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Anatolij M. Plichko, David Yost (2000)
Extracta Mathematicae
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Does a given Banach space have any non-trivial complemented subspaces? Usually, the answer is: yes, quite a lot. Sometimes the answer is: no, none at all.