Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On certain geometric properties in Banach spaces of vector-valued
  functions   We consider a certain type of geometric properties of Banach spaces, which
includes for instance octahedrality, almost squareness, lushness and the
Daugavet property. For this type of properties, we obtain a general reduction
theorem, which, roughly speaking, states the following: if the property in
question is stable under certain finite absolute sums (for example finite
$\ell^p$-sums), then it is also stable under the formation of corresponding
K\"othe-Bochner spaces (for example $L^p$-Bochner spaces). From this general
theorem, we obtain as corollaries a number of new results as well as some
alternative proofs of already known results concerning octahedral and almost
square spaces and their relatives, diameter-two-properties, lush spaces and
other classes.

24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph