摘要
设A是含单位元I和非平凡投影P的*-代数,满足:若XAP={0},则X=0;且若XA(I-P)={0},则X=0.本文证明了φ是A上的非线性A^(*)B-B^(*)A型导子当且仅当φ是可加的*-导子.并将这个结果应用到素*-代数、无中心和的I1型von Neumann代数、因子von Neumann代数和标准算子代数.
Let A be a unital*-algebra with the unit I and a nontrivial projection P.Suppose that A satisfies XAP={0}implies X=0 and XA(I−P)={0}implies X=0.We prove thatis a nonlinear A*B−B*A type derivation on A if and only ifis an additive*-derivation.This is then applied to prime*-algebra,von Neumann algebras of type I1 with no central summands,factor von Neumann algebras and standard operator algebras.
作者
张芳娟
ZHANG Fangjuan(School of Science,Xi’an University of Posts and Telecommunications,Xi’an,Shaanxi,710121,P.R.China)
出处
《数学进展》
CSCD
北大核心
2024年第2期367-380,共14页
Advances in Mathematics（China）
基金
Supported by NSFC(No.11601420)
Natural Science Basic Research Plan in Shaanxi Province(No.2018JM1053)。
