Separable injectivity and \(C^*\) tensor products (Q757794)

The notion of separable injectivity for \(C^*\)-algebras has been introduced in \textit{R. R. Smith} and \textit{D. P. Williams} [Indian Univ. Math. J. 37, 111-133 (1988; Zbl 0628.46057)]. The main result of the paper under review is as follows. The minimal \(C^*\)-tensor product of \(C^*\)-algebras A and B is separably injective if and only if A and B are separably injective and either A or B is finite dimensional. This is the analog of a result, due to M. Takesaki, for injective \(C^*\)- algebras.