Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Operator amenability of the Fourier algebra in the cb-multiplier norm   Let $G$ be a locally compact group, and let $A_\cb(G)$ denote the closure of
$A(G)$, the Fourier algebra of $G$, in the space of completely bounded
multipliers of $A(G)$. If $G$ is a weakly amenable, discrete group such that
$\cstar(G)$ is residually finite-dimensional, we show that $A_\cb(G)$ is
operator amenable. In particular, $A_\cb(F_2)$ is operator amenable even though
$F_2$, the free group in two generators, is not an amenable group. Moreover, we
show that, if $G$ is a discrete group such that $A_\cb(G)$ is operator
amenable, a closed ideal of $A(G)$ is weakly completely complemented in $A(G)$
if and only if it has an approximate identity bounded in the cb-multiplier
norm.

19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga