Structure of nested sequences of balls in Banach spaces

Pradipta Bandyopadhyay, Vladimir P. Fonf, Bor Luh Lin, Miguel Martín

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


In this paper, we study the structure of the union of unbounded nested sequences of balls, and use them to characterize some geometric properties of X*. We show that the union of an unbounded nested sequence of balls is a cone if the centers of the balls lie in a finite dimensional subspace. However, in general, such a union need not be a cone. In fact, examples can be constructed, up to renorming, in any infinite dimensional Banach space. We also study when such an union is the intersection of at most k half-spaces, and relate it with the number of extreme points of any face of the dual ball.

Original languageEnglish
Pages (from-to)173-193
Number of pages21
JournalHouston Journal of Mathematics
Issue number1
StatePublished - 1 Jan 2003


  • Extreme points
  • Nested sequences of balls
  • Rotund points

ASJC Scopus subject areas

  • General Mathematics


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