Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Improving integrability via absolute summability: a general version of
  Diestel's Theorem   A classical result by J. Diestel establishes that the composition of a
summing operator with a (strongly measurable) Pettis integrable function gives
a Bochner integrable function. In this paper we show that a much more general
result is possible regarding the improvement of the integrability of vector
valued functions by the summability of the operator. After proving a general
result, we center our attention in the particular case given by the
$(p,\sigma)$-absolutely continuous operators, that allows to prove a lot of
special results on integration improvement for selected cases of classical
Banach spaces ---including $C(K)$, $L^p$ and Hilbert spaces--- and operators
---$p$-summing, $(q,p)$-summing and $p$-approximable operators---.

4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th