@misc{10481/76695,
year = {2021},
month = {12},
url = {http://hdl.handle.net/10481/76695},
abstract = {Let A and B be Banach algebras with bounded approximate identities
and let F: A→B be a surjective continuous linear map which preserves twosided
zero products (i.e., F(a)F(b) = F(b)F(a) = 0 whenever ab = ba = 0).
We show that F is a weighted Jordan homomorphism provided that A is zero
product determined and weakly amenable. These conditions are in particular
fulfilled when A is the group algebra L1(G) with G any locally compact group.
We also study a more general type of continuous linear maps F : A → B that
satisfy F(a)F(b)+F(b)F(a) = 0 whenever ab = ba = 0. We show in particular
that if F is surjective and A is a C∗-algebra, then F is a weighted Jordan
homomorphism.},
organization = {Slovenian Research Agency - Slovenia	P1-0288},
organization = {MCIU/AEI/FEDER Grant	PGC2018-093794-B-I00},
organization = {Junta de Andalucia	FQM-185	
P20_00255	
MIU	FPU18/00419	
EST19/00466},
organization = {Proyectos I+D+i del programa operativo FEDER-Andalucia Grant	A-FQM-484-UGR18},
publisher = {Elsevier},
keywords = {Zero product determined Banach algebra},
keywords = {Weakly amenable Banach algebra},
keywords = {Group algebra of a locally compact group},
keywords = {C∗-algebra},
keywords = {Algebra of approximable operators},
keywords = {Weighted Jordan homomorphism},
keywords = {Two-sided zero products},
keywords = {Linear preserver},
title = {Maps preserving two-sided zero products on Banach algebras},
author = {Bresar, M. and Castillo Godoy, María Luisa and Villena Muñoz, Armando Reyes},
}