ISOMETRIES OF JB-ALGEBRAS

A bijective linear mapping between two JB-algebras A and B is an isome try if and only if it commutes with the Jordan triple products of A an d B. Other algebraic characterizations of isometries between JB-algebr as are given. Derivations on a JB-algebra A are those bounded linear o perators on A with zero numerical range. For JB-algebras of selfadjoin t operators we have: If H and K are left Hilbert spaces of dimension g reater than or equal to 3 over the same field F (the real, complex, or quaternion numbers), then every surjective real linear isometry f fro m S(H) onto S(K) is of the form f(x) = U o x o U-1 for x in S(H), wher e tau is a real-linear automorphism of F and U is a real linear isomet ry from H onto K with U(lambda h) = tau(lambda)U(h) for lambda in F an d h in H.