Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Full factors and co-amenable inclusions   We show that if $M$ is a full factor and $N \subset M$ is a co-amenable
subfactor with expectation, then $N$ is also full. This answers a question of
Popa from 1986. We also generalize a theorem of Tomatsu by showing that if $M$
is a full factor and $\sigma \colon G \curvearrowright M$ is an outer action of
a compact group $G$, then $\sigma$ is automatically minimal and $M^G$ is a full
factor which has w-spectral gap in $M$. Finally, in the appendix, we give a
proof of the fact that several natural notions of co-amenability for an
inclusion $N\subset M$ of von Neumann algebras are equivalent, thus closing the
cycle of implications given in Anantharaman-Delaroche's paper in 1995.

6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph