Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tensor Products of Convex Cones, Part II: Closed Cones in
  Finite-Dimensional Spaces   In part I, we studied tensor products of convex cones in dual pairs of real
vector spaces. This paper complements the results of the previous paper with an
overview of the most important additional properties in the finite-dimensional
case. (i) We show that the projective cone can be identified with the cone of
positive linear operators that factor through a simplex cone. (ii) We prove
that the projective tensor product of two closed convex cones is once again
closed (Tam already proved this for proper cones). (iii) We study the tensor
product of a cone with its dual, leading to another proof (and slight
extension) of a theorem of Barker and Loewy. (iv) We provide a large class of
examples where the projective and injective cones differ. As this paper was
being written, this last result was superseded by a result of Aubrun, Lami,
Palazuelos and Pl\'avala, who independently showed that the projective cone
$E_+ \mathbin{\otimes_\pi} F_+$ is strictly contained in the injective cone
$E_+ \mathbin{\otimes_\varepsilon} F_+$ whenever $E_+$ and $F_+$ are closed,
proper and generating, with neither $E_+$ nor $F_+$ a simplex cone. Compared to
their result, this paper only proves a few special cases.

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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin