Higher *-derivations between unital C*-algebras

Surveys in Mathematics and its Applications

关键词: Alternative fixed point;    Hyers--Ulam--Rassias stability;    Higher *-derivation;   

DOI  :  

来源: DOAJ

【 摘 要 】

Let A, B be two unital C^*-algebras.We prove that every sequence of mappings from A into B, H = {h₀,h₁, ..., h_m, ...}, which satisfy h_m(3ⁿuy) =Σ_i+j=mh_i(3ⁿu)h_j(y) for each m ∈ N₀, for all u∈U(A), all y∈ A, and all n = 0, 1, 2, ..., is a higher derivation. Also, for a unital C^*-algebra A of real rank zero, every sequence of continuous mappings from A into B, H = {h₀,h₁,..., h_m, ...}, is a higher derivation when h_m(3ⁿuy)=Σ_i+j=mh_i(3ⁿu)h_j(y) holds for all u∈I₁(A_sa), all y∈ A, all n = 0, 1,2, ... and for each m ∈ N₀. Furthermore, by using the fixed points methods, we investigate the Hyers-Ulam-Rassias stability of higher *-derivations between unital C^*-algebras.

【 授权许可】

Unknown