@misc{10481/71128,
year = {2021},
month = {9},
url = {http://hdl.handle.net/10481/71128},
abstract = {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.},
organization = {MCIU/AEI/FEDER Grant	PGC2018-093794-B-I00},
organization = {Junta de Andalucia	FQM-185},
organization = {Proyectos I+D+i del programa operativo FEDER-Andalucia Grant	A-FQM-484-UGR18},
organization = {MIU PhD scholarship Grant	FPU18/00419},
organization = {Universidad de Granada/CBUA},
publisher = {Elsevier},
keywords = {Zero product determined Banach algebra},
keywords = {Group algebra},
keywords = {Algebra of approximable operators},
title = {Strongly zero product determined Banach algebras},
doi = {10.1016/j.laa.2021.09.002},
author = {Alaminos Prats, Jerónimo and Extremera Lizana, José and Castillo Godoy, María Luisa and Villena Muñoz, Armando Reyes},
}