Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Boundedness and surjectivity in Banach spaces   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.

1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ