Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A survey on the interplay between arithmetic mean ideals, traces,
  lattices of operator ideals, and an infinite Schur-Horn majorization theorem   The work of Dykema, Figiel, Weiss, and Wodzicki on the structure of
commutators showed that arithmetic means play an important role in the study of
operator ideals, and we explored their role in a multipaper project which we
survey in this article. We start by presenting the notions of arithmetic mean
ideals and arithmetic mean at infinity ideals. Then we explore their
connections with commutator spaces, traces, elementary operators, lattice and
sublattice structure of ideals, arithmetic mean ideal cancellation properties
of first and second order, and softness properties - a term that we introduced
but a notion ubiquitous in the literature on operator ideals. Arithmetic mean
closure of ideals leads us to investigate majorization for infinite sequences
and this in turn leads us to an infinite Schur-Horn majorization theorem which
extends theorems by A. Neumann, by Arveson and Kadison, and by Antezana,
Massey, Ruiz and Stojanoff. We also list ten open questions that we encountered
in the development of this material.

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The categories of this paper are: physics
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The categories of this paper are: cs
34
The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: supr-con
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The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: funct-an