*-代数上ξ-*-Jordan-型非线性导子

数学物理学报 ›› 2022, Vol. 42 ›› Issue (4): 1003-1017.

-代数上ξ--Jordan-型非线性导子

张芳娟^1,*(),朱新宏²

¹ 西安邮电大学理学院西安 710121
² 西安现代控制技术研究所西安 710065

收稿日期:2021-09-10 出版日期:2022-08-26 发布日期:2022-08-08
通讯作者: 张芳娟 E-mail:zhfj888@xupt.edu.cn; zhfj888@126.com
基金资助:
国家自然科学基金(11601420);和陕西省自然科学基础研究计划资助基金(2018JM1053)

Nonlinear ξ--Jordan-Type Derivations on -Algebras

Fangjuan Zhang^1,*(),Xinhong Zhu²

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)

摘要/Abstract

摘要：

设${\cal A}$是含单位元$I$的$*$- 代数且$\xi$是非零复数. 假设${\cal A}$包含非平凡投影$P, $满足: 若$X{\cal A} P=0, $则$X=0;$若$X{\cal A}(I- P)=0, $则$X=0.$如果$\phi$是${\cal A}$上的非线性$\xi$-$*$-Jordan- 型导子当且仅当$\phi$是可加的$*$- 导子, 且对所有的$A\in{\cal A}, $有$\phi(\xi A)=\xi\phi(A)$.

关键词: ξ-*-Jordan- 型导子, *- 代数, *- 导子

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

中图分类号:

O177.1

张芳娟, 朱新宏. *-代数上ξ-*-Jordan-型非线性导子[J]. 数学物理学报, 2022, 42(4): 1003-1017.

Fangjuan Zhang, Xinhong Zhu. Nonlinear ξ-*-Jordan-Type Derivations on *-Algebras[J]. Acta mathematica scientia,Series A, 2022, 42(4): 1003-1017.

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