Separate weak\(^*\)-continuity of the triple product in dual real JB\(^*\)-triples (Q1581831)

\textit{J. M. Isodro, W. Kaup} and \textit{A. Rodríguez Palacio} [Manuscr. Math. 86, 311-335 (1995; Zbl 0834.17047)] introduced a concept of real JB*-triple as a real form of a complex JB*-triple. The class of real JB*-triples include all JB-algebras, all real \(C^*\)-algebras, all J*B-algebras and obviously all complex JB*-triples. In this paper we prove that, if \(E\) is a real JB*-triple having a predual \(E_*\), then \(E_*\) is the unique predual of \(E\) and the triple product on \(E\) is separately \(\sigma(E,E_*)\)-continuous, extending the important result due to \textit{T. Barton} and \textit{R. M. Timoney} for complex JB*-triples [Math. Scand. 59, 177-191 (1986; Zbl 0621.46044)].