International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 4, Pages 717-723

Nuclear JC-algebras and tensor products of types

Fatmah B. Jamjoom

Department of Mathematics, King Saud University, Riyadh 11431, Saudi Arabia

Received 7 April 1992; Revised 12 June 1992

Copyright © 1993 Fatmah B. Jamjoom. 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.


This article is a continuation of [1], to which the reader is referred for the definition and properties of the JC-tensor product of two JC-algebras. Our standard references for nuclear and postliminal C*-algebras are [2,3,4,5,6,7]. We extend the notion of nuclearity to JC-algebras and prove that postliminal JC-algebras are nuclear. In contrast with the situation which occurs for C*-algebras, the JC-tensor product of two postliminal JC-algebras turns out, in general, to be non-postliminal and can even be anitliminal.