The Jordan Algebra of Complex Symmetric Operators
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| Titel: | The Jordan Algebra of Complex Symmetric Operators |
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| Autoren: | Wang, Cun, Zhu, Sen |
| Quelle: | Chinese Annals of Mathematics, Series B. 46:733-758 |
| Publication Status: | Preprint |
| Verlagsinformationen: | Springer Science and Business Media LLC, 2025. |
| Publikationsjahr: | 2025 |
| Schlagwörter: | 46L70, 47C10, 47B99, Mathematics - Operator Algebras, FOS: Mathematics, 0101 mathematics, Operator Algebras (math.OA), 01 natural sciences |
| Beschreibung: | For a conjugation $C$ on a separable, complex Hilbert space $\mathcal{H}$, the set $\mathcal{S}_C$ of $C$-symmetric operators on $\mathcal{H}$ forms a weakly closed, selfadjoint, Jordan operator algebra. In this paper we study $\mathcal{S}_C$ in comparison with the algebra $\mathcal{B(H)}$ of all bounded linear operators on $\mathcal{H}$, and obtain $\mathcal{S}_C$-analogues of some classical results concerning $\mathcal{B(H)}$. We determine the Jordan ideals of $\mathcal{S}_C$ and their dual spaces. Jordan automorphisms of $\mathcal{S}_C$ are classified. We determine the spectra of Jordan multiplication operators on $\mathcal{S}_C$ and their different parts. It is proved that those Jordan invertible ones constitute a dense, path connected subset of $\mathcal{S}_C$. 24 pages |
| Publikationsart: | Article |
| Sprache: | English |
| ISSN: | 1860-6261 0252-9599 |
| DOI: | 10.1007/s11401-025-0039-7 |
| DOI: | 10.48550/arxiv.1912.10391 |
| Zugangs-URL: | http://arxiv.org/abs/1912.10391 |
| Rights: | Springer Nature TDM arXiv Non-Exclusive Distribution |
| Dokumentencode: | edsair.doi.dedup.....5423faeddf22ec4b1ee69f1ae4eb4148 |
| Datenbank: | OpenAIRE |
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Nájsť tento článok vo Web of Science | Abstract: | For a conjugation $C$ on a separable, complex Hilbert space $\mathcal{H}$, the set $\mathcal{S}_C$ of $C$-symmetric operators on $\mathcal{H}$ forms a weakly closed, selfadjoint, Jordan operator algebra. In this paper we study $\mathcal{S}_C$ in comparison with the algebra $\mathcal{B(H)}$ of all bounded linear operators on $\mathcal{H}$, and obtain $\mathcal{S}_C$-analogues of some classical results concerning $\mathcal{B(H)}$. We determine the Jordan ideals of $\mathcal{S}_C$ and their dual spaces. Jordan automorphisms of $\mathcal{S}_C$ are classified. We determine the spectra of Jordan multiplication operators on $\mathcal{S}_C$ and their different parts. It is proved that those Jordan invertible ones constitute a dense, path connected subset of $\mathcal{S}_C$.<br />24 pages |
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| ISSN: | 18606261 02529599 |
| DOI: | 10.1007/s11401-025-0039-7 |