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Characterization of linear mappings on (Banach) ⋆-algebras by similar properties to derivations
Mathematica Slovaca ( IF 0.654 ) Pub Date : 2020-07-24 , DOI: 10.1515/ms-2017-0409
Behrooz Fadaee; Kamal Fallahi; Hoger Ghahramani

Let 𝓐 be a ⋆-algebra, δ : 𝓐 → 𝓐 be a linear map, and z ∈ 𝓐 be fixed. We consider the condition that δ satisfies (y) + δ(x)y = δ(z) (x δ(y) + δ(x) y = δ(z)) whenever xy = z (x y = z), and under several conditions on 𝓐, δ and z we characterize the structure of δ. In particular, we prove that if 𝓐 is a Banach ⋆-algebra, δ is a continuous linear map, and z is a left (right) separating point of 𝓐, then δ is a Jordan derivation. Our proof is based on complex variable techniques. Also, we describe a linear map δ satisfying the above conditions with z = 0 on two classes of ⋆-algebras: zero product determined algebras and standard operator algebras.
更新日期:2020-08-09

 

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