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Abstract
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.
Author information
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FG
F. Garcia
Dep. de Matemáticas, Fac. de Matemáticas, Universidad de Murcia, 30.100 Espinardo -- Murcia, Spain
Inst. of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Street, Block 8, 1113 Sofia, Bulgaria, and Dep. de Matemáticas, Fac. de Matemáticas, Universidad de Murcia, 30.100 Espinardo -- Murcia, Spain
F. Garcia, L. Oncina, J. Orihuela, S. Troyanski. “Kuratowski's Index of Non-Compactness and Renorming in Banach Spaces.” Journal of Convex Analysis 11 (2004), No. 2, 477–494.