The facial and inner ideal structure of a real JBW\(^*\)-triple (Q2711602)

According to the approach of Isidro, Kaup and Rodríguez Palacios, a real \(\text{JB}^*\)-triple \(B\) is a closed real subtriple of a (complex) \(\text{JB}^*\)-triple \(A\), and a real \(\text{JBW}^*\)-triple is a real \(\text{JB}^*\)-triple the canonical hermitification \(A\) of which is a \(\text{JBW}^*\)-triple. The structure of such real \(\text{JBW}^*\)-triples is the aim of the paper under review. Results, previously obtained by the authors for \(\text{JBW}^*\)-triples, as those relating the algebraic structure of a \(\text{JBW}^*\)-triple \(A\) to the geometric structure of the unit balls in \(A\) and in its predual, as well as that showing that every weak\(^*\)-closed inner ideal in \(A\) is the range of a unique structural projection on \(A\), are here extending to real \(\text{JBW}^*\)-triples.