On the lifting property for \(C^{\ast}\)-algebras
Summary: We characterize the lifting property (LP) of a separable \(C^{\ast}\)-algebra \(A\) by a property of its maximal tensor product with other \(C^{\ast}\)-algebras, namely we prove that \(A\) has the LP of and only if for any family \(\{D_i \mid i \in I\}\) of \(C^{\ast}\)-algebras the canonical map \(\ell_{\infty}(\{D_i\}) \oplus_{\max} A \to \ell_{\infty}(\{D_i \oplus_{\max} A\})\) is isometric. Equivalently, this holds if and only if \(M \oplus_{\max} A = M \oplus_{\mathrm{nor}} A\) for any von Neumann algebra \(M\).
scientific article; zbMATH DE number 7629322
scientific article