Relative Weak Injectivity for C*-algebras

2016/10/27 by Ali S. Kavruk, Kavruk, Ali Samil · 1 citation
Mathematics · #46L06 46L07 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1610.08599

openalex publication_date 2016/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Nuclearity-related properties for nonselfadjoint algebras
• Pullback and Pushout Constructions in C*-Algebra Theory

Cited by

• Relative Weak Injectivity for Operator Systems

Related

• Relative weak injectivity of operator system pairs
• Order theory and interpolation in operator algebras
• Arveson's extension theorem in *-algebras
• Relative Weak Injectivity for Operator Systems
• Omitting types in operator systems