Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Commutators and linear spans of projections in certain finite
  C*-algebras   Assume that A is a unital separable simple C*-algebra with real rank zero,
stable rank one, strict comparison of projections, and that its tracial simplex
T(A) has a finite number of extremal points.
  We prove that every self-adjoint element a in A in the kernel of all tracial
states is the sum of two commutators in A and that every positive element of A
is a linear combination of projections with positive coefficients.
  Assume that A is as above but \sigma-unital. Then an element (resp. a
positive element) a of A is a linear combination (resp. a linear combination
with positive coefficients) of projections if and only if for all \tau in T(A),
the extension \bar\tau to the enveloping von Neumann algebra has a finite value
for the range projection of a.
  Assume that A is unital and as above but T(A) has infinitely many extremal
points. Then A is not the linear span of its projections. This result settles
two open problems of Marcoux.

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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: patt-sol
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The categories of this paper are: quant-ph
3
The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: eess