Nuclear JC-algebras and tensor products of types

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.