Boundedness and surjectivity in Banach spaces

Details Boundedness and surjectivity in Banach spaces Boundedness and surjectivity in Banach spaces

2000-09-04

arxiv.org/abs/math/0009034v1

Mathematics

Functional Analysis

15 pages

Scientific paper

We define the ($w^\ast$-) boundedness property and the ($w^\ast$-) 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 ($w^\ast$-) thickness. We give examples of interesting sets having or not having these properties. In particular, we prove that the tensor product of two $w^\ast$-thick sets in $\Xastast$ and $\Yast$ is a $w^\ast$-thick subset in $L(X,Y)^\ast$ and obtain as a concequense that the set $w^\ast -exp\:B_{K(l_2)^\ast}$ is $w^\ast$-thick.

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