On a non-commutative analogue of a classical result of Namioka and Phelps

A. Samil Kavruk

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arXiv · 1412.7936

On a non-commutative analogue of a classical result of Namioka and Phelps

A. Samil Kavruk

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Abstract

A classical result of Namioka and Phelps states that the square is a test object to verify semi-simplexity in the tensor theory of convex compact sets. By using the quantization of generalized Namioka-Phelps test spaces we formulate a nuclearity criteria for C*-algebras, which establishes a non-commutative version of their result. The proof we suggest covers the nuclearity characterization via non-commutative polyhedron outlined by Effros. Several matrix systems studied by Farenick and Paulsen are shown to be test systems for nuclearity. We also prove that the standard Namioka-Phelps test space is C*-nuclear. We propose a partition of unity property for C*-algebras which distinguishes nuclear C*-algebras among the others.

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A. Samil Kavruk. 2014-12-26. On a non-commutative analogue of a classical result of Namioka and Phelps. https://arxiv.org/abs/1412.7936

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