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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A characterization of inner ideals in $ {\rm JB}\sp *$-triples


Authors: C. M. Edwards and G. T. Rüttimann
Journal: Proc. Amer. Math. Soc. 116 (1992), 1049-1057
MSC: Primary 46L70
DOI: https://doi.org/10.1090/S0002-9939-1992-1102856-1
MathSciNet review: 1102856
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Abstract: It is shown that a norm-closed subtriple $ B$ of a $ J{B^ * }$-triple $ A$ is an inner ideal if and only if every bounded linear functional on $ B$ has a unique norm-preserving extension to a bounded linear functional on $ A$. It follows that the norm-closed subtriples $ B$ of a $ {C^ * }$-algebra $ A$ that enjoy this unique extension property are precisely those of the form $ e{A^{ * * }}f \cap A$ where $ (e,f)$ is a pair of centrally equivalent open projections in the $ {W^ * }$-envelope $ {A^{ * * }}$ of $ A$.


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DOI: https://doi.org/10.1090/S0002-9939-1992-1102856-1
Keywords: $ J{B^ * }$-triple, inner ideal
Article copyright: © Copyright 1992 American Mathematical Society