Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dense nuclear Fr\'echet ideals in $C^\star$-algebras   We show that a $C^\star$-algebra $B$ contains a dense left or right Fr\'echet
ideal $A$, with $A$ a nuclear locally convex space, if and only if the
primitive ideal space Prim$(B)$ of $B$ is discrete and countable, and $B/I$ is
finite dimensional for each $I \in $ Prim$(B)$. We show the forward implication
holds for a general Banach algebra $B$, if the ideal is assumed two-sided. For
$C^\star$-algebras, we construct all two-sided dense nuclear ideals by defining
a set of matrix-valued Schwartz functions on the countable discrete space
Prim$(B)$.

15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat