International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 1, Pages 139-147
doi:10.1155/S0161171291000133
Separable injectivity and C*-tensor products
Tadasi Huruya1
and Seung-Hyeok Kye2
1Faculty of Education, Niigata University, Niigata 950-21, Japan
2Department of Mathematics, Song Sim College for Women, Bucheon, Seoul 422-743, Korea
Abstract
Let A and B be C*-algebras and let D be a C*-subalgebra of B. We show that if D is separably injective then the triple (A,B,D) verifies the slice map conjecture. As an application, we prove that the minimal C*-tensor product A⊗B is separably injective if and only if both A and B are separably injective and either A or B is finite-dimensional.