Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decomposibility and norm convergence properties in finite von Neumann
  algebras   We study Schur-type upper triangular forms for elements, T, of von Neumann
algebras equipped with faithful, normal, tracial states. These were introduced
in a paper of Dykema, Sukochev and Zanin; they are based on Haagerup-Schultz
projections. We investigate when the s.o.t.-quasinilpotent part of this
decomposition of T is actually quasinilpotent. We prove implications involving
decomposability and strong decomposability of T. We show this is related to
norm convergence properties of the sequence |T^n|^{1/n} which, by a result of
Haagerup and Schultz, is known to converge in strong operator topology. We
introduce a Borel decomposability, which is a property appropriate for elements
of finite von Neumann algebras, and show that the circular operator is Borel
decomposable. We also prove the existence of a thin-spectrum
s.o.t.-quasinilpotent operator in the hyperfinite II_1-factor.

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The categories of this paper are: q-bio
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The categories of this paper are: math-ph
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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: ao-sci
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex