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International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 1, Pages 139-147
http://dx.doi.org/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 Hindawi Publishing Corporation. 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 AB is separably injective if and only if both A and B are separably injective and either A or B is finite-dimensional.