Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (4): 1003-1017.

Previous Articles     Next Articles

Nonlinear ξ-*-Jordan-Type Derivations on *-Algebras

Fangjuan Zhang1,*(),Xinhong Zhu2   

  1. 1 School of Science, Xi'an University of Posts and Telecommunications, Xi'an 710121
    2 Xi'an Modern Control Technology Institute, Xi'an 710065
  • Received:2021-09-10 Online:2022-08-26 Published:2022-08-08
  • Contact: Fangjuan Zhang E-mail:zhfj888@xupt.edu.cn; zhfj888@126.com
  • Supported by:
    the NSFC(11601420);the Natural Science Basic Research Plan in Shaanxi Province(2018JM1053)

Abstract:

Let ${\cal A}$ be a unital $*$-algebra with the unit $I$ and let $\xi\in{\Bbb C}\setminus\{0\}.$ Assume that ${\cal A}$ contains a nontrivial projection $P$ which satisfies $X{\cal A} P=0$ implies $X=0$ and $X{\cal A}(I-P)=0$ implies $X=0.$ Then $\phi$ is a nonlinear $\xi$-$*$-Jordan-type derivations on ${\cal A}$ if and only if $\phi$ is an additive $*$-derivation and $\phi(\xi A)=\xi\phi(A)$ for all $A\in{\cal A}.$

Key words: ξ-*-Jordan-type derivation, *-Algebra, *-Derivation

CLC Number: 

  • O177.1
Trendmd