Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Closed ideals with bounded $\Delta$-weak approximate identities in some
  certain Banach algebras   It is shown that a locally compact group $G$ is amenable if and only if some
certain closed ideals of the Fig\`{a}-Talamanca-Herz algebra $A_{p}(G)$ admit
bounded $\Delta$-weak approximate identities. Also, similar results are
obtained for the function algebras $\mathfrak{L}A(G)$ and $C_{0}^{w}(G)$.

31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex