Kuratowski's Index of Non-Compactness and Renorming in Banach Spaces
Journal of convex analysis, Tome 11 (2004) no. 2, pp. 477-494
Cet article a éte moissonné depuis 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
@article{JCA_2004_11_2_JCA_2004_11_2_a11,
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},
year = {2004},
volume = {11},
number = {2},
url = {http://geodesic.mathdoc.fr/item/JCA_2004_11_2_JCA_2004_11_2_a11/}
}
TY - JOUR AU - F. Garcia AU - L. Oncina AU - J. Orihuela AU - S. Troyanski TI - Kuratowski's Index of Non-Compactness and Renorming in Banach Spaces JO - Journal of convex analysis PY - 2004 SP - 477 EP - 494 VL - 11 IS - 2 UR - http://geodesic.mathdoc.fr/item/JCA_2004_11_2_JCA_2004_11_2_a11/ ID - JCA_2004_11_2_JCA_2004_11_2_a11 ER -
%0 Journal Article %A F. Garcia %A L. Oncina %A J. Orihuela %A S. Troyanski %T Kuratowski's Index of Non-Compactness and Renorming in Banach Spaces %J Journal of convex analysis %D 2004 %P 477-494 %V 11 %N 2 %U http://geodesic.mathdoc.fr/item/JCA_2004_11_2_JCA_2004_11_2_a11/ %F JCA_2004_11_2_JCA_2004_11_2_a11
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/