The fixed point property in -triples and preduals of -triples

We prove that for every member X in the class of real or complex JB ∗ -triples or preduals of JBW ∗ -triples, the following assertions are equivalent:(1) the fixed point property. the super fixed point property. normal structure. uniform normal structure. nach space of X is reflexive. consequence, a real or complex C ∗ -algebra or the predual of a real or complex W ∗ -algebra having the fixed point property must be finite-dimensional.