Abstract. We prove that, if E is a real JB*-triple having a predual E * , then E * is the unique predual of E and the triple product on E is separately σ(E, E * )−continuous. Mathematics Subject Classification (1991):17C65, 46K70, 46L05, 46L10, 46L70

No abstract

No abstract

In [19], R. Kadison proved that every surjective linear isometry $\Phi{:}\, {\C A} \to {\C B}$ between two unital C*-algebras has the form $$\Phi (x) = u T (x), \hbox{ $x\in {\C A}$,}$$ where $u$ is a unitary element in ${\C B}$ and $T$ is a Jordan *-isomorphism from${\C A}$ onto ${\C B}$. This result extends the classical Banach–Stone theorem [3, 32] obtained in the 1930s to non-abelian unital C*-algebras. A. L. Paterson and A. M. Sinclair extended Kadison's result to surjective isometries between C*-algebras by replacing the unitary element $u$ by a unitary element in the multiplier C*-algebra of the range algebra [28]. Thus, every surjective linear isometry between C*-algebras preserves the triple products as $$\J xyz \,{=}\, 2^{-1} ( x y^* z + z y^* x).$$

No abstract