Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conditional positive definiteness as a bridge between k-hyponormality
  and n-contractivity   For sequences $\alpha \equiv \{\alpha_n\}_{n=0}^{\infty}$ of positive real
numbers, called weights, we study the weighted shift operators $W_{\alpha}$
having the property of moment infinite divisibility ($\mathcal{MID}$); that is,
for any $p > 0$, the Schur power $W_{\alpha}^p$ is subnormal. We first prove
that $W_{\alpha}$ is $\mathcal{MID}$ if and only if certain infinite matrices
$\log M_{\gamma}(0)$ and $\log M_{\gamma}(1)$ are conditionally positive
definite (CPD). Here $\gamma$ is the sequence of moments associated with
$\alpha$, $M_{\gamma}(0),M_{\gamma}(1)$ are the canonical Hankel matrices whose
positive semi-definiteness determines the subnormality of $W_{\alpha}$, and
$\log$ is calculated entry-wise (i.e., in the sense of Schur or Hadamard).
Next, we use conditional positive definiteness to establish a new bridge
between $k$--hyponormality and $n$--contractivity, which sheds significant new
light on how the two well known staircases from hyponormality to subnormality
interact. As a consequence, we prove that a contractive weighted shift
$W_{\alpha}$ is $\mathcal{MID}$ if and only if for all $p>0$, $M_{\gamma}^p(0)$
and $M_{\gamma}^p(1)$ are CPD.

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The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
13
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: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: nlin
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th