Central kernels of subspaces of JB∗-triples

An investigation of the norm central kernel kn(L) of an arbitrary norm-closed subspace L of a JB∗-triple and the central kernel k(L) of a weak∗-closed subspace L of a JBW∗-triple is carried out. It is shown that these geometrically defined objects have purely algebraic characterizations, the results providing new information about C∗-algebras and W∗-algebras.