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Proceedings of the American Mathematical Society

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Real isometries between $ {\rm JB}\sp *$-triples


Author: T. Dang
Journal: Proc. Amer. Math. Soc. 114 (1992), 971-980
MSC: Primary 46L70; Secondary 17C65, 46L05
DOI: https://doi.org/10.1090/S0002-9939-1992-1056677-9
MathSciNet review: 1056677
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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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DOI: https://doi.org/10.1090/S0002-9939-1992-1056677-9
Article copyright: © Copyright 1992 American Mathematical Society

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