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
1Faculty of Education, Niigata University, Niigata 950-21, Japan
2Department of Mathematics, Song Sim College for Women, Bucheon, Seoul 422-743, Korea
Received 26 January 1990
Copyright © 1991 Tadasi Huruya and Seung-Hyeok Kye. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.