Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebras of Toeplitz operators on the $n$-dimensional unit ball   We study $C^*$-algebras generated by Toeplitz operators acting on the
standard weighted Bergman space $\mathcal{A}_{\lambda}^2(\mathbb{B}^n)$ over
the unit ball $\mathbb{B}^n$ in $\mathbb{C}^n$. The symbols $f_{ac}$ of
generating operators are assumed to be of a certain product type. By choosing
$a$ and $c$ in different function algebras $\mathcal{S}_a$ and $\mathcal{S}_c$
over lower dimensional unit balls $\mathbb{B}^{\ell}$ and
$\mathbb{B}^{n-\ell}$, respectively, and by assuming the invariance of $a\in
\mathcal{S}_a$ under some torus action we obtain $C^*$-algebras
$\boldsymbol{\mathcal{T}}_{\lambda}(\mathcal{S}_a, \mathcal{S}_c)$ whose
structural properties can be described. In the case of $k$-quasi-radial
functions $\mathcal{S}_a$ and bounded uniformly continuous or vanishing
oscillation symbols $\mathcal{S}_c$ we describe the structure of elements from
the algebra $\boldsymbol{\mathcal{T}}_{\lambda}(\mathcal{S}_a, \mathcal{S}_c)$,
derive a list of irreducible representations of
$\boldsymbol{\mathcal{T}}_{\lambda}(\mathcal{S}_a, \mathcal{S}_c)$, and prove
completeness of this list in some cases. Some of these representations
originate from a `quantization effect', induced by the representation of
$\mathcal{A}_{\lambda}^2(\mathbb{B}^n)$ as the direct sum of Bergman spaces
over a lower dimensional unit ball with growing weight parameter. As an
application we derive the essential spectrum and index formulas for
matrix-valued operators.

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The categories of this paper are: hep-th
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: cs
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-ex