2018/02/20 by Ali S. Kavruk, Kavruk, Ali S.
Mathematics · #46L05 #46L06 #46L07 #47L25 #47L90 #Advanced Operator Algebra Research #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1802.06917
openalex publication_date 2018/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the notion of relative weak injectivity and its nuclearity related properties in the category of operator systems. We obtain several characterizations of the weak expectation property. We show that (c,max)-nuclearity characterizes Kirchberg and Wasserman's C*-systems. Namioka and Phelps' test systems, which detects nuclear C*-algebras, is shown to characterize nuclear C*-systems. We study quasi-nuclearity in the operator system setting and prove that quasi-nuclearity and nuclearity are equivalent, in other words, (er,max)-nuclearity and (min,max)-nuclearity are equivalent.