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arXiv · 1610.08599

Relative Weak Injectivity for C*-algebras

Ali Samil Kavruk
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Abstract

We study the order theoretic properties of relative weak injectivity, w.r.i., in short, in the category of C*-algebras. We prove that Arveson's extension theorem, with additional order assumption on the morphisms, is tightly connected with relative weak injectivity. We prove that (2,3)-Riesz-Arveson property, defined below, is equivalent to w.r.i. Likewise tight Riesz interpolation property yields another characterization of w.r.i. We exhibit, with examples, that these C*-algebraic properties fail in general operator systems. Several order theoretic characterization of Connes' embedding problem is given.

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Ali Samil Kavruk. 2016-10-27. Relative Weak Injectivity for C*-algebras. https://arxiv.org/abs/1610.08599

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