Classification of sequentially weakly continuous \(JB^*\)-triples (Q1568205)

A \(JB^{\star }\)-triple \(A\) is said to be a sequentially weakly continuous if every biholomorphic automorphism of the unit ball of \(A\) is sequentially weakly continuous. The main result of this paper asserts that a \(JB^{\star }\)-triple \(A\) is sequentially weakly continuous if an only if the following conditions hold: (i) all primitive ideals of \(A\) are maximal; and (ii) the bidual \(A^{\star \star }\) is a \(JBW^{\star }\)-triple of type I without infinite spin part. Some consequences for the general structure of the \(JB^{\star }\)-triples are obtained.