Bilinear maps having Jordan product property
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| Titel: | Bilinear maps having Jordan product property |
|---|---|
| Autoren: | Jorge J. Garcés, Mykola Khrypchenko |
| Quelle: | Linear Algebra and its Applications. 728:435-448 |
| Publication Status: | Preprint |
| Verlagsinformationen: | Elsevier BV, 2026. |
| Publikationsjahr: | 2026 |
| Schlagwörter: | Operator Algebras, Primary: 15A86, 47C15, 17C65, secondary: 17A36, 47B47, Rings and Algebras, Rings and Algebras (math.RA), FOS: Mathematics, Operator Algebras (math.OA) |
| Beschreibung: | We study symmetric continuous bilinear maps $V$ on a C$^*$-algebra $A$ that have the Jordan product property at a fixed element $z\in A$. We show that, whenever $A$ is a finite direct sum or a $c_0$-sum of infinite simple von Neumann algebras, such a map $V$ has the square-zero property. Then, it is proved that $V(a,b)=T(a\circ b)$ for some bounded linear map $T$ on $A$. As a consequence, Jordan homomorphisms and derivations at $z\in A$ are characterized. |
| Publikationsart: | Article |
| Sprache: | English |
| ISSN: | 0024-3795 |
| DOI: | 10.1016/j.laa.2025.09.013 |
| DOI: | 10.48550/arxiv.2508.09052 |
| Zugangs-URL: | http://arxiv.org/abs/2508.09052 |
| Rights: | Elsevier TDM arXiv Non-Exclusive Distribution |
| Dokumentencode: | edsair.doi.dedup.....0197a92d71bf08e2806be9cfed748bfb |
| Datenbank: | OpenAIRE |
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Nájsť tento článok vo Web of Science | Abstract: | We study symmetric continuous bilinear maps $V$ on a C$^*$-algebra $A$ that have the Jordan product property at a fixed element $z\in A$. We show that, whenever $A$ is a finite direct sum or a $c_0$-sum of infinite simple von Neumann algebras, such a map $V$ has the square-zero property. Then, it is proved that $V(a,b)=T(a\circ b)$ for some bounded linear map $T$ on $A$. As a consequence, Jordan homomorphisms and derivations at $z\in A$ are characterized. |
|---|---|
| ISSN: | 00243795 |
| DOI: | 10.1016/j.laa.2025.09.013 |