International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 4, Pages 717-723
doi:10.1155/S0161171293000894
Nuclear JC-algebras and tensor products of types
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.
Abstract
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.