We introduce a certain property of commutative Banach algebras which we call property . We prove that every bounded disjointness-preserving linear map from a commutative Banach algebra with the aforesaid property to any semisimple, commutative Banach algebra is a weighted composition map. Further, it is shown that a variety of important Banach algebras in harmonic analysis have the property .
"Disjointness-preserving linear maps on Banach function algebras associated with a locally compact group." Ann. Funct. Anal. 7 (3) 442 - 451, August 2016. https://doi.org/10.1215/20088752-3605573