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.
Covering spheres of Banach spaces by balls / V.P. Fonf, C. Zanco. - In: MATHEMATISCHE ANNALEN. - ISSN 0025-5831. - 344:4(2009 Aug), pp. 939-945. [10.1007/s00208-009-0336-6]
Covering spheres of Banach spaces by balls
C. ZancoUltimo
2009
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.
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