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Zero Jordan Product Determined Banach Algebras
A Banach algebra A is said to be a zero Jordan product determined Banach algebra if, for every Banach space X, every bilinear map φ:A×A→X satisfying φ(a,b)=0 whenever a, b∈A are such that ab+ba=0, is of the form φ(a,b)=σ(ab+ba) for some continuous linear map σ. We show that all C∗-algebras and all group algebras L1(G) of amenable locally compact groups have this property and also discuss some applications.
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