Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Preduals for spaces of operators involving Hilbert spaces and
  trace-class operators   Continuing the study of preduals of spaces $\mathcal{L}(H,Y)$ of bounded,
linear maps, we consider the situation that $H$ is a Hilbert space. We
establish a natural correspondence between isometric preduals of
$\mathcal{L}(H,Y)$ and isometric preduals of $Y$.
  The main ingredient is a Tomiyama-type result which shows that every
contractive projection that complements $\mathcal{L}(H,Y)$ in its bidual is
automatically a right $\mathcal{L}(H)$-module map.
  As an application, we show that isometric preduals of
$\mathcal{L}(\mathcal{S}_1)$, the algebra of operators on the space of
trace-class operators, correspond to isometric preduals of $\mathcal{S}_1$
itself (and there is an abundance of them). On the other hand, the compact
operators are the unique predual of $\mathcal{S}_1$ making its multiplication
separately weak* continuous.

9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org