Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Weak Expectation Property and Riesz Interpolation   We show that Lance's weak expectation property is connected to tight Riesz
interpolations in lattice theory. More precisely we first prove that if A
\subset B(H) is a unital C*-subalgebra, where B(H) is the bounded linear
operators on a Hilbert space H, then A has (2,2) tight Riesz interpolation
property in B(H) (defined below). An extension of this requires an additional
assumption on A: A has (2,3) tight Riesz interpolation property in B(H) at
every matricial level if and only if A has the weak expectation property.
  Let $J = span{(1,1,-1,-1,-1)}$ in $C^5$ . We show that a unital C*-algebra A
has the weak expectation property if and only if $A \otimesmin (C^5/J) = A
\otimesmax (C^5/J)$ (here \otimesmin and \otimesmax are the minimal and the
maximal operator system tensor products, respectively, and $C^5/J$ is the
operator system quotient of $C^5$ by $J$).
  We express the Kirchberg conjecture (KC) in terms of a four dimensional
operator system problem. We prove that KC has an affirmative answer if and only
if $C^5/J$ has the double commutant expectation property if and only if $C5/J
\otimesmin C5/J = C5/J \otimesc C5/J$ (here \otimesc represents the commuting
operator system tensor product).

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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: physics
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The categories of this paper are: atom-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: eess
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: cs
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The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con