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arXiv · 2508.09052

Bilinear maps having Jordan product property

Jorge J. Garcés·Mykola Khrypchenko
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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.

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Jorge J. Garcés, Mykola Khrypchenko. 2025-08-12. Bilinear maps having Jordan product property. https://doi.org/10.1016/j.laa.2025.09.013

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