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  1. ; ; ; (, Mathematische Nachrichten)
    Abstract In a recent paper, we showed that a subspace of a real ‐triple is an ‐summand if and only if it is a ‐closed triple ideal. As a consequence, ‐ideals of real ‐triples, including real ‐algebras, real ‐algebras and real TROs, correspond to norm‐closed triple ideals. In this paper, we extend this result by identifying the ‐ideals in (possibly non‐self‐adjoint) real operator algebras and Jordan operator algebras. The argument for this is necessarily different. We also give simple characterizations of one‐sided ‐ideals in real operator algebras, and give some applications to that theory. 
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