Journal of the Ramanujan Mathematical Society

Volume 41, Issue 2, June 2026 pp. 105–112.

On mappings preserving commutative zero products

Authors: Abbas Zivari-Kazempour
Author institution:Department of Mathematics, Faculty of Basic Sciences, Ayatollah Boroujerdi University, Boroujerd, Iran.

Summary: Let f be a continuous linear map between Banach algebras A and B satisfying f (a ⚬ b) = f (a) ⚬ f (b) for all a, b ∈ A with ab = ba = 0. In this paper, under special hypothesis we prove that f is a Jordan homomorphism. We also characterize derivable maps that preserves commutative zero products. Finally, we determine continuous linear maps which preserves idempotents products, that is, f (ab) = f (a) f (b) for all a, b ∈ A with ab = p, where p is an idempotent in A.

Contents Full-Text PDF