M-ideals in real operator algebras
Operator Algebras
2025-02-19 v2 Functional Analysis
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.
Keywords
Cite
@article{arxiv.2405.05383,
title = {M-ideals in real operator algebras},
author = {David P. Blecher and Matthew Neal and Antonio M. Peralta and Shanshan Su},
journal= {arXiv preprint arXiv:2405.05383},
year = {2025}
}
Comments
18 pages, to appear Math Nachrichten