Boundedness and surjectivity in normed spaces

Olav Nygaard

International Journal of Mathematics and Mathematical Sciences, 2002, vol. 32, 1-17

Abstract:

We define the ( w * -) boundedness property and the ( w * -) surjectivity property for sets in normed spaces. We show that these properties are pairwise equivalent in complete normed spaces by characterizing them in terms of a category-like property called ( w * -) thickness. We give examples of interesting sets having or not having these properties. In particular, we prove that the tensor product of two w * -thick sets in X * * and Y * is a w * -thick subset in L ( X , Y ) * and obtain as a consequence that the set w * - exp B K ( l 2 ) * is w * -thick.

Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:467357

DOI: 10.1155/S0161171202011596

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