Bilinear maps having Jordan product property

2025/08/12 by Garcés, Jorge J., Khrypchenko, Mykola
#17C65 #47B47 #47C15 #FOS: Mathematics #Operator Algebras (math.OA) #Primary: 15A86 #Rings and Algebras (math.RA) #secondary: 17A36

paper · doi:10.48550/arxiv.2508.09052

Abstract

We study symmetric continuous bilinear maps V on a C^*-algebra A that have the Jordan product property at a fixed element z∈ A. We show that, whenever A is a finite direct sum or a c₀-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∘ b) for some bounded linear map T on A. As a consequence, Jordan homomorphisms and derivations at z∈ A are characterized.

Citations

• Maps preserving two-sided zero products on Banach algebras
• Jordan weak amenability and orthogonal forms on JB*-algebras

Related

• Bilinear maps on C^*-algebras that have product property at a compact element
• Zero product preservers of C*-algebras
• Maps preserving two-sided zero products on Banach algebras
• Characterizing linear mappings through zero products or zero Jordan products
• *-Jordan-type maps on C^*-algebras