Covering spheres of Banach spaces by balls

Vladimir P. Fonf, Clemente Zanco

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

If the unit sphere of a Banach space X can be covered by countably many balls no one of which contains the origin, then, as an easy consequence of the separation theorem, X*is w*-separable. We prove the converse under suitable renorming. Moreover, the balls of the countable covering can be chosen as translates of the same ball.

Original languageEnglish
Pages (from-to)939-945
Number of pages7
JournalMathematische Annalen
Volume344
Issue number4
DOIs
StatePublished - 1 Aug 2009

ASJC Scopus subject areas

  • Mathematics (all)

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