On the lifting property for C *-algebras

摘要

We characterize the lifting property (LP) of a separable C *-algebra A by a property of its maximal tensor product with other C*-algebras, namely we prove that A has the LP if and only if for any family {Di I i E I} of C *-algebras the canonical map tOO({Di }) (R) max A-* tOO({Di (R) max A}) is isometric. Equivalently, this holds if and only if M (R) max A = M (R) nor A for any von Neumann algebra M.