Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a Class of Ideals of the Toeplitz Algebra on the Bergman Space of the
  Unit Ball   Let $\mathfrak{T}$ denote the full Toeplitz algebra on the Bergman space of
the unit ball $\mathbb{B}_n.$ For each subset $G$ of $L^{\infty},$ let
$\mathfrak{CI}(G)$ denote the closed two-sided ideal of $\mathfrak{T}$
generated by all $T_fT_g-T_gT_f$ with $f,g\in G.$ It is known that
$\mathfrak{CI}(C(\bar{\mathbb{B}}_n))=\mathcal{K}$ - the ideal of compact
operators and $\mathfrak{CI}(C(\mathbb{B}_n))=\mathfrak{T}.$ Despite these
``extremal cases'', $\mathfrak{T}$ does contain other non-trivial ideals. This
paper gives a construction of a class of subsets $G$ of $L^{\infty}$ so that
$\mathcal{K}\subsetneq\mathfrak{CI}(G)\subsetneq\mathfrak{T}.$

33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int