Abstract
We formulate and prove Bell’s inequalities in the realm of JB \(^*\) triples and JB \(^*\) algebras. We show that the maximal violation of Bell’s inequalities occurs in any JBW \(^*\) triple containing a nonassociative \(2\) -Peirce subspace. Moreover, we show that the violation of Bell’s inequalities in a nonmodular JBW \(^*\) algebra and in an essentially nonmodular JBW \(^*\) triple is generic. We describe the structure of maximal violators and its relation to the spin factor. In addition, we present a synthesis of available results based on a unified geometric approach.
