Compact-like manifolds associated to J B*-triples

Finite dimensional JB*-triples have a uniquely associated simply connected compact symmetric manifold. In infinite dimensions, different constructions have been used to yield three possibly different Banach manifolds from a J B*-triple all of which display compact like behaviour. We clarify the relat ionship between these three manifolds and characterise a case when all thre e of these manifolds coincide as in the finite dimensional case. These resu lts have been announced in [11].