Li, Weihua On ultraproducts of operator algebras. (English) Zbl 1123.46040 Sci. China, Ser. A 48, No. 9, 1284-1295 (2005). Summary: Some basic questions on ultraproducts of \(C^*\)-algebras and von Neumann algebras are considered, including the relation to \(K\)-theory of \(C^*\)-algebras. More specifically, we prove that under certain conditions, the \(K\)-groups of ultraproducts of \(C^*\)-algebras are isomorphic to the ultraproduct of respective \(K\)-groups of \(C^*\)-algebras. We also show that the ultraproducts of factors of type \(\text{II}_1\) are prime, i.e., not isomorphic to any nontrivial tensor product. Cited in 3 Documents MSC: 46L05 General theory of \(C^*\)-algebras 46L10 General theory of von Neumann algebras 46L80 \(K\)-theory and operator algebras (including cyclic theory) Keywords:ultraproducts of \(C^*\)-algebras; \(K\)-theory; ultraproducts of factors PDFBibTeX XMLCite \textit{W. Li}, Sci. China, Ser. A 48, No. 9, 1284--1295 (2005; Zbl 1123.46040)