Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence structures and Hausdorff uo-Lebesgue topologies on vector
  lattice algebras of operators   A vector sublattice of the order bounded operators on a Dedekind complete
vector lattice can be supplied with the convergence structures of order
convergence, strong order convergence, unbounded order convergence, strong
unbounded order convergence, and, when applicable, convergence with respect to
a Hausdorff uo-Lebesgue topology and strong convergence with respect to such a
topology. We determine the general validity of the implications between these
six convergences on the order bounded operator and on the orthomorphisms.
Furthermore, the continuity of left and right multiplications with respect to
these convergence structures on the order bounded operators, on the order
continuous operators, and on the orthomorphisms is investigated, as is their
simultaneous continuity. A number of results are included on the equality of
adherences of vector sublattices of the order bounded operators and of the
orthomorphisms with respect to these convergence structures. These are
consequences of more general results for vector sublattices of arbitrary
Dedekind complete vector lattices. The special attention that is paid to vector
sublattices of the orthomorphisms is motivated by explaining their relevance
for representation theory on vector lattices.

34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph