Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tensorial Function Theory: From Berezin transforms to Taylor's Taylor
  series and back   Let $H^{\infty}(E)$ be the Hardy algebra of a $W^{*}$-correspondence $E$ over
a $W^{*}$-algebra $M$. Then the ultraweakly continuous completely contractive
representations of $H^{\infty}(E)$ are parametrized by certain sets
$\mathcal{AC}(\sigma)$ indexed by $NRep(M)$ - the normal *-representations
$\sigma$ of $M$. Each set $\mathcal{AC}(\sigma)$ has analytic structure, and
each element $F\in H^{\infty}(E)$ gives rise to an analytic operator-valued
function $\hat{F}_{\sigma}$ on $\mathcal{AC}(\sigma)$ that we call the
$\sigma$-Berezin transform of $F$. The sets
${\mathcal{AC}(\sigma)}_{\sigma\in\Sigma}$ and the family of functions
${\hat{F}_{\sigma}}_{\sigma\in\Sigma}$ exhibit "matricial structure" that was
introduced by Joeseph Taylor in his work on noncommutative spectral theory in
the early 1970s. Such structure has been exploited more recently in other areas
of free analysis and in the theory of linear matrix inequalities. Our objective
here is to determine the extent to which the matricial structure characterizes
the Berezin transforms.

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The categories of this paper are: adap-org
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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: q-bio
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The categories of this paper are: math-ph
7
The categories of this paper are: hep-th