M$M$‐Ideals in real operator algebras
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.
Authors
- David P. Blecher (ORCID: https://orcid.org/0000-0003-2093-2289)
- Antonio M. Peralta (ORCID: https://orcid.org/0000-0003-2528-8357)
- Matthew Neal (ORCID: https://orcid.org/0000-0002-7986-6370)
- Shanshan Su
Institutions
- East China University of Science and Technology (CN)
- Universidad de Granada (ES)
- Denison University (US)
- University of Houston (US)
Publication Details
- Journal
- Mathematische Nachrichten
- Published
- 2025-03-04
- DOI
- https://doi.org/10.1002/mana.202400227
- Primary Topic
- Advanced Topics in Algebra
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Science Foundation
- Simons Foundation
- Ministry of Science and Technology of the People's Republic of China
- Junta de Andalucía