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arXiv · 2405.05383

M-ideals in real operator algebras

David P. Blecher·Matthew Neal·Antonio M. Peralta·Shanshan Su
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Abstract

In a recent paper we showed that a subspace of a real JBW*-triple is an M-summand if and only if it is a weak*-closed triple ideal. As a consequence, M-ideals of real JB*-triples, including real C*-algebras, real JB*-algebras and real TROs, correspond to norm-closed triple ideals. In the present paper we extend this result to (possibly non-selfadjoint) real operator algebras and Jordan operator algebras, where the argument is necessarily different. We also give simple characterizations of one-sided M-ideals in real operator algebras, and give some applications to that theory.

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David P. Blecher, Matthew Neal, Antonio M. Peralta, Shanshan Su. 2024-05-08. M-ideals in real operator algebras. https://arxiv.org/abs/2405.05383

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