Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Alternative Estimate for the Numerical Radius of Hilbert Space
  Operators   We give an alternative lower bound for the numerical radii of Hilbert space
operators. As a by-product, we find conditions such that
  \begin{equation*} \omega\left(\left[\begin{array}{cc} 0 & R \\ S & 0
\end{array}\right]\right)=\frac{\Vert R \Vert +\Vert S\Vert }{2}
\end{equation*} where $R, S \in \mathbb{B}(\mathcal{H})$.

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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: cs
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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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: q-bio
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The categories of this paper are: stat
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The categories of this paper are: bayes-an