Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A non-hyponormal operator generating Stieltjes moment sequences   A linear operator $S$ in a complex Hilbert space $\hh$ for which the set
$\dzn{S}$ of its $C^\infty$-vectors is dense in $\hh$ and $\{\|S^n
f\|^2\}_{n=0}^\infty$ is a Stieltjes moment sequence for every $f \in \dzn{S}$
is said to generate Stieltjes moment sequences. It is shown that there exists a
closed non-hyponormal operator $S$ which generates Stieltjes moment sequences.
What is more, $\dzn{S}$ is a core of any power $S^n$ of $S$. This is
established with the help of a weighted shift on a directed tree with one
branching vertex. The main tool in the construction comes from the theory of
indeterminate Stieltjes moment sequences. As a consequence, it is shown that
there exists a non-hyponormal composition operator in an $L^2$-space (over a
$\sigma$-finite measure space) which is injective, paranormal and which
generates Stieltjes moment sequences. In contrast to the case of abstract
Hilbert space operators, composition operators which are formally normal and
which generate Stieltjes moment sequences are always subnormal (in fact
normal). The independence assertion of Barry Simon's theorem which
parameterizes von Neumann extensions of a closed real symmetric operator with
deficiency indices $(1,1)$ is shown to be false.

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The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: physics
11
The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con