Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The weighted mean matrix with weight sequence $w_n=2n+1$ is a hyponormal
  operator on $\ell^2$   A weighted mean matrix whose weight sequence is linear with positive
coefficients is shown to be a posinormal operator on $\ell^2$. This operator is
also shown to be coposinormal, so it and its adjoint have the same null space
and the same range. The posinormality result leads to a proof that the weighted
mean matrix associated with the sequence of odd positive integers is
hyponormal, as well as a conjecture regarding a more general linear case.

4
The categories of this paper are: cond-mat
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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: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: nlin
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The categories of this paper are: astro-ph