Real isometries between 𝐽𝐵*-triples

Dang, T.

doi:10.1090/S0002-9939-1992-1056677-9

Real isometries between $\textrm {JB}^ *$-triples
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Proc. Amer. Math. Soc. 114 (1992), 971-980 Request permission

Abstract:

It is shown that except for a certain class of JB*-triples (for which the result is false), real linear surjective isometries preserve the triple product. In particular, unital real linear isometries of ${C^*}$-algebras are real linear Jordan $^*$-isomorphisms.

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