Bilinear maps having Jordan product property
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917002554114048 |
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| author | Garcés, Jorge J. Khrypchenko, Mykola |
| author_facet | Garcés, Jorge J. Khrypchenko, Mykola |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_09052 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bilinear maps having Jordan product property Garcés, Jorge J. Khrypchenko, Mykola Operator Algebras Rings and Algebras Primary: 15A86, 47C15, 17C65, secondary: 17A36, 47B47 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. |
| title | Bilinear maps having Jordan product property |
| topic | Operator Algebras Rings and Algebras Primary: 15A86, 47C15, 17C65, secondary: 17A36, 47B47 |
| url | https://arxiv.org/abs/2508.09052 |