Compact-like manifolds associated to JB*-triples

Finite dimensional JB ^ast;-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 JB ^ast; all of which display compact like behaviour. We clarify the relationship between these three manifolds and characterise a case when all three of these manifolds coincide as in the finite dimensional case. These results have been announced in [11]. Received: 29 May 2001