Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Schur-Horn Problem for Normal Operators   We consider the Schur-Horn problem for normal operators in von Neumann
algebras, which is the problem of characterizing the possible diagonal values
of a given normal operator based on its spectral data. For normal matrices,
this problem is well-known to be extremely difficult, and in fact, it remains
open for matrices of size greater than $3$. We show that the infinite
dimensional version of this problem is more tractable, and establish
approximate solutions for normal operators in von Neumann factors of type
I$_\infty$, II and III. A key result is an approximation theorem that can be
seen as an approximate multivariate analogue of Kadison's Carpenter Theorem.

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The categories of this paper are: quant-ph
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The categories of this paper are: cs
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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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: chem-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph