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

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• 作者：A. Samil Kavruk ^{kavruk@illinois.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 46L06 ; 46L07 ; secondary ; 46L05 ; 47L25 ; 47L90
• 刊名：Journal of Functional Analysis
• 出版年：2015
• 出版时间：15 November 2015
• 年：2015
• 卷：269
• 期：10
• 页码：3282-3303
• 全文大小：430 K

文摘

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 criterion for C^鈦?/sup>${\mathrm{C}}^{鈦?/mo>}$-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 [8]. Several matrix systems studied by Farenick and Paulsen [13] are shown to be test systems for nuclearity. We also prove that the standard Namioka–Phelps test space is C^鈦?/sup>${\mathrm{C}}^{鈦?/mo>}$-nuclear. We propose a partition of unity property for C^鈦?/sup>${\mathrm{C}}^{鈦?/mo>}$-algebras which distinguishes nuclear C^鈦?/sup>${\mathrm{C}}^{鈦?/mo>}$-algebras among the others.