Characterization of multipliers on ⋆-algebras acting on orthogonal elements

Let A be a Banach ⋆-algebra, X be a Banach ⋆-A-bimodule and T : A −→ X be a continuous linear map. In this paper, by using orthogonality conditions on A, we characterize the map T on certain Banach algebra including C ⋆ -algebras, group algebras, standard operator algebras and Banach algebras that is generated by idempotents. We also characterize a continuous linear map from zero Jordan product determined Banach algebra A into a Banach A-bimodule X, and give some applications of this result.