Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Commutant Lifting for Commuting Row Contractions   If $T= \big[ T_1 ... T_n\big]$ is a row contraction with commuting entries,
and the Arveson dilation is $\tilde T= \big[ \tilde T_1 ... \tilde T_n\big]$,
then any operator $X$ commuting with each $T_i$ dilates to an operator $Z$ of
the same norm which commutes with each $\tilde T_i$.

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The categories of this paper are: q-bio
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The categories of this paper are: econ
32
The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-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