Geodesic
Kuratowski's Index of Non-Compactness and Renorming in Banach Spaces
Journal of convex analysis, Tome 11 (2004) no. 2, pp. 477-494.

Voir la notice de l'article provenant de la source Heldermann Verlag

A point x in A, where A is a subset of the metric space (X, || . ||), is quasi-denting if for every ε > 0 there exists a slice of A containing x with Kuratowski index less than ε. The aim of this paper is to generalize the following theorem of L. S. Troyanski [Israel J. Math. 88 (1994) 175--188] with a geometric approach: A Banach space such that every point of the unit sphere is quasi-denting (for the unit ball) admits an equivalent LUR norm.
Mots-clés : Quasi-denting points, Kuratowski's index, LUR renorming 
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     author = {F. Garcia and L. Oncina and J. Orihuela and S. Troyanski},
     title = {Kuratowski's {Index} of {Non-Compactness} and {Renorming} in {Banach} {Spaces}},
     journal = {Journal of convex analysis},
     pages = {477--494},
     publisher = {mathdoc},
     volume = {11},
     number = {2},
     year = {2004},
     url = {http://geodesic.mathdoc.fr/item/JCA_2004_11_2_JCA_2004_11_2_a11/}
}
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F. Garcia; L. Oncina; J. Orihuela; S. Troyanski. Kuratowski's Index of Non-Compactness and Renorming in Banach Spaces. Journal of convex analysis, Tome 11 (2004) no. 2, pp. 477-494. http://geodesic.mathdoc.fr/item/JCA_2004_11_2_JCA_2004_11_2_a11/