Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the order structure of representable functionals   The main purpose of this paper is to investigate some natural problems
regarding the order structure of representable functionals on $^*$-algebras. We
describe the extreme points of order intervals, and give a nontrivial
sufficient condition to decide whether or not the infimum of two representable
functionals exists. To this aim we offer a suitable approach to the Lebesgue
decomposition theory, which is in complete analogy with the one developed by
Ando in the context of positive operators. This tight analogy allows to invoke
Ando's results to characterize uniqueness of the decomposition, and solve the
infimum problem over certain operator algebras.

7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph