Nonlinear η-∗-Jordan n-Derivation on ∗-Algebras
Abstract
Let A be a unital ∗-algebra with the unit I over the complex field C and let η≠0,±1 be a complex number. For any A,B∈A, A⋄ηB=AB+ηBA* is referred to as the η-Jordan ∗-product. Suppose that n≥3 is a fixed positive integer. In this study, it is shown that if a map φ:A→A satisfies φ(A1⋄ηA2⋄η⋯⋄ηAn)=∑k=1nA1⋄η⋯⋄ηAk−1⋄ηφ(Ak)⋄ηAk+1⋄η⋯⋄ηAn for all A1,A2⋯An−3∈{I,iI} and An−2,An−1,An∈A, then φ is an additive ∗-derivation and φ(ηA)=ηφ(A) for all A∈A, where i is the imaginary unit. In application, characterizations of prime ∗-algebras, von Neumann algebras with no central summands of type I1 and factor von Neumann algebras are obtained.
Fields of Study & Subjects
Advanced Topics in Algebra
Advanced Operator Algebra Research
Functional Equations Stability Results
Publication details
- Journal / source
- Mathematics
- Publisher
- MDPI AG
- Volume
- 14
- Issue
- 3
- Pages
- 449–449
- Publication date
- 27 January 2026
- Language
- EN