Zero jordan product determined Banach algebras Alaminos Prats, Jerónimo Bresar, M. Extremera Lizana, José Villena Muñoz, Armando Reyes C*-algebras Group algebra Zero Jordan product determined Banach algebra Zero product determined Banach algebra Symmetrically amenable Banach algebra Weakly amenable Banach algebra The authors were supported by MINECO grant PGC2018-093794-B-I00. The first, the third and the fourth named authors were supported by Junta de Andalucia grant FQM-185. The second named author was supported by ARRS grant P1-0288. A Banach algebra A is said to be a zero Jordan product determined Banach algebra if, for every Banach space X, every bilinear map phi : A x A -> X satisfying phi(a, b) = 0 whenever a, b is an element of A are such that ab + ba = 0, is of the form phi(a, b) = sigma(ab + ba) for some continuous linear map sigma. We show that all C*-algebras and all group algebras L-1(G) of amenable locally compact groups have this property and also discuss some applications. 2021-10-15T10:41:16Z 2021-10-15T10:41:16Z 2019-02-13 info:eu-repo/semantics/article Published version: ALAMINOS, J... [et al.] (2021). ZERO JORDAN PRODUCT DETERMINED BANACH ALGEBRAS. Journal of the Australian Mathematical Society, 111(2), 145-158. doi:[10.1017/S1446788719000478] http://hdl.handle.net/10481/70884 eng http://creativecommons.org/licenses/by-nc-nd/3.0/es/ info:eu-repo/semantics/openAccess Atribución-NoComercial-SinDerivadas 3.0 España Cambridge University