On the Manifold of Complemented Principal Inner Ideals in JB*-Triples

The set 필 of Neher's classes of tripotents in an arbitrary JB*-triple Z is considered and a natural complex-analytic Banach manifold structure is defined on it. The relationship between 필 and the Grassmann manifold of all complemented principal inner ideals in Z is studied in detail, and the smooth complete vector fields on 필 are characterized as smooth complete equivariant vector fields on the manifold M of tripotents of Z.