Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal domain of $q$-concave operators and vector measure
  representation of $q$-concave Banach lattices   Given a Banach space valued $q$-concave linear operator $T$ defined on a
$\sigma$-order continuous quasi-Banach function space, we provide a description
of the optimal domain of $T$ preserving $q$-concavity, that is, the largest
$\sigma$-order continuous quasi-Banach function space to which $T$ can be
extended as a $q$-concave operator. We show in this way the existence of
maximal extensions for $q$-concave operators. As an application, we show a
representation theorem for $q$-concave Banach lattices through spaces of
integrable functions with respect to a vector measure. This result culminates a
series of representation theorems for Banach lattices using vector measures
that have been obtained in the last twenty years.

16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph