Relative Weak Injectivity for Operator Systems

Abstract: 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.