Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hilbert $C^*$-modules over $\Sigma^*$-algebras   A $\Sigma^*$-algebra is a concrete $C^*$-algebra that is sequentially closed
in the weak operator topology. We study an appropriate class of $C^*$-modules
over $\Sigma^*$-algebras analogous to the class of $W^*$-modules (selfdual
$C^*$-modules over $W^*$-algebras), and we are able to obtain
$\Sigma^*$-versions of virtually all the results in the basic theory of $C^*$-
and $W^*$-modules. In the second half of the paper, we study modules possessing
a weak sequential form of the condition of being countably generated. A
particular highlight of the paper is the "$\Sigma^*$-module completion," a
$\Sigma^*$-analogue of the selfdual completion of a $C^*$-module over a
$W^*$-algebra, which has an elegant uniqueness condition in the countably
generated case.

25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio