On nicely smooth Banach spaces.
Pradipta Bandyopadhyay, Sudeshna Basu (2001)
Extracta Mathematicae
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Pradipta Bandyopadhyay, Sudeshna Basu (2001)
Extracta Mathematicae
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J. Talponen (2007)
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M. Fabian, V. Zizler (2001)
Extracta Mathematicae
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Plichko, Anatolij (1997)
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* This paper was supported in part by the Bulgarian Ministry of Education, Science and Technologies under contract MM-506/95. The main results of the paper are: Theorem 1. Let a Banach space E be decomposed into a direct sum of separable and reflexive subspaces. Then for every Hausdorff locally convex topological vector space Z and for every linear continuous bijective operator T : E → Z, the inverse T^(−1) is a Borel map. Theorem 2. Let us assume the continuum hypothesis....
Robert Deville (2006)
RACSAM
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We survey recent results on the structure of the range of the derivative of a smooth real valued function f defined on a real Banach space X and of a smooth mapping F between two real Banach spaces X and Y. We recall some necessary conditions and some sufficient conditions on a subset A of L(X,Y) for the existence of a Fréchet-differentiable mapping F from X into Y so that F'(X) = A. Whenever F is only assumed Gâteaux-differentiable, new phenomena appear: we discuss the existence of...
Gilles Godefroy (2001)
Extracta Mathematicae
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Gilles Lancien (2006)
RACSAM
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We describe how the Szlenk index has been used in various areas of the geometry of Banach spaces. We cover the following domains of application of this notion: non existence of universal spaces, linear classification of C(K) spaces, descriptive set theory, renorming problems and non linear classification of Banach spaces.
Abdelhakim Maaden (2001)
Extracta Mathematicae
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Zarghami, R. (2010)
The Journal of Nonlinear Sciences and its Applications
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M. Isabel Garrido, Jesús A. Jaramillo (2002)
Extracta Mathematicae
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