Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Cuntz Semigroup and Comparison of Open Projections   We show that a number of naturally occurring comparison relations on positive
elements in a C*-algebra are equivalent to natural comparison properties of
their corresponding open projections in the bidual of the C*-algebra. In
particular we show that Cuntz comparison of positive elements corresponds to a
comparison relation on open projections, that we call Cuntz comparison, and
which is defined in terms of-and is weaker than-a comparison notion defined by
Peligrad and Zsid\'o. The latter corresponds to a well-known comparison
relation on positive elements defined by Blackadar. We show that Murray-von
Neumann comparison of open projections corresponds to tracial comparison of the
corresponding positive elements of the C*-algebra. We use these findings to
give a new picture of the Cuntz semigroup.

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The categories of this paper are: gr-qc
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The categories of this paper are: q-bio
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin