Approximately n--Jordan derivations: A fixed point approach

2009/08/03 by Ali Ebadian, A. Ebadian, Ebadian, A.
Mathematics · #39B52 #46HXX #Advanced Topics in Algebra #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Functional Equations Stability Results #math.FA #msc:39B52 #msc:46HXX

paper · pdf · doi:10.48550/arxiv.0908.0295

arxiv created 2009/08/03 · openalex publication_date 2009/08/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let n∈ \Bbb N-\1\, and let A be a Banach algebra. An additive map D: A→ A is called n-Jordan derivation if D(aⁿ)=D(a)a^n-1+aD(a)a^n-2+...+a^n-2D(a)a+a^n-1D(a), for all a ∈ A. Using fixed point methods, we investigate the stability of n--Jordan derivations (n--Jordan ^*-derivations) on Banach algebras (C^*-algebras). Also we show that to each approximate ^*-Jordan derivation f in a C^*- algebra there corresponds a unique ^*-derivation near to f.

Citations

• On the stability of the linear mapping in Banach spaces

Related

• Nearly generalized Jordan derivations
• Jordan derivations on certain Banach algebras
• n-Jordan homomorphisms
• Characterizations of (m,n)-Jordan derivations on some algebras
• Jordan derivations on the θ-Lau products of Banach algebras