Strongly zero product determined Banach algebras Alaminos Prats, Jerónimo Extremera Lizana, José Castillo Godoy, María Luisa Villena Muñoz, Armando Reyes Zero product determined Banach algebra Group algebra Algebra of approximable operators The authors were supported by MCIU/AEI/FEDER Grant PGC2018-093794-B-I00, Junta de Andalucia grant FQM-185. The first, second and fourth authors were supported by Proyectos I+D+i del programa operativo FEDER-Andalucia Grant A-FQM-484-UGR18. The third named author was also supported by MIU PhD scholarship Grant FPU18/00419. Funding for open access charge: Universidad de Granada/CBUA. C*-algebras, group algebras, and the algebra A(X) of approximable operators on a Banach space Xhaving the bounded approximation property are known to be zero product determined. In this paper we give a quantitative estimate of this property by showing that, for the Banach algebra A, there exists a constant awith the property that for every continuous bilinear functional phi: A x A -> C there exists a continuous linear functional xi on A such that sup(parallel to a parallel to=parallel to b parallel to=1) vertical bar phi(a, b) - xi(ab)vertical bar <= alpha sup(parallel to a parallel to=parallel to b parallel to=1ab-0), vertical bar phi(a, b)vertical bar in each of the following cases: (i) Ais a C*-algebra, in which case alpha = 8; (ii) A = L-1(G) for a locally compact group G, in which case alpha = 60 root 271+sin pi/10/1-2sin pi/10; (iii) A = A(X) for a Banach space Xhaving property (A)(which is a rather strong approximation property for X), in which case alpha = 60 root 27 1+sin pi/10/1-2sin pi/10 C-2, where C is a constant associated with the property(A) that we require forX. 2021-10-27T08:33:24Z 2021-10-27T08:33:24Z 2021-09-06 info:eu-repo/semantics/article J. Alaminos... [et al.]. Strongly zero product determined Banach algebras, Linear Algebra and its Applications, Volume 630, 2021, Pages 326-354, ISSN 0024-3795, [https://doi.org/10.1016/j.laa.2021.09.002] http://hdl.handle.net/10481/71128 10.1016/j.laa.2021.09.002 eng http://creativecommons.org/licenses/by-nc-nd/3.0/es/ info:eu-repo/semantics/openAccess Atribución-NoComercial-SinDerivadas 3.0 España Elsevier