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Let T: A→B be a (not necessarily surjective) linear isometry between two real JB*-triples. Then for each a∈A, there exists a tripotent ua in the bidual, B″, of B such that {ua, T({f, g, h}), ua}={ua, {T(f), T(g), T(h)}, ua}, for all f, g, h in the real JB*-subtriple, Aa, generated by a; the mapping {ua, T(·), ua}:Aa→B″ is a linear isometry. Furthermore, when B is a real C*-algebra, the projection ...

LINEAR ISOMETRIES BETWEEN REAL JB*-TRIPLES AND C*-ALGEBRAS

LINEAR ISOMETRIES BETWEEN REAL JB-TRIPLES AND C-ALGEBRAS