2011/11/25 by Mahmood Alaghmandan, Alaghmandan, Mahmood, Rasoul Nasr-Isfahani +3
Mathematics · #43A20 #43A22 #43A25 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:43A20 #msc:43A22 #msc:43A25
paper · pdf · doi:10.48550/arxiv.1111.5922
Gradual improvements in the pervious version led to this version which covers all the results of the previous one while it studies commutative Banach algebras instead of just one specific class
openalex publication_date 2011/11/25 · arxiv created 2013/10/31 · arxiv updated 2013/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \cal A and \cal B be Banach algebras. A linear map T:\cal A → \cal B is called separating or disjointness preserving if ab=0 implies Ta Tb = 0 for all a,b∈ \cal A. In this paper, we study a new class of regular Tauberian algebras and prove that some well-known Banach algebras in harmonic analysis belong to this class. We show that a bijective separating map between these algebras turns out to be continuous and the maximal ideal spaces of underlying algebras are homeomorphic. By imposing extra conditions on these algebras, we find a more thorough characterization of separating maps. The existence of a bijective separating map also leads to the existence of an algebraic isomorphism in some cases.