Let A be a unital^(*)-algebra with the unit I and a nontrivial projection P∈A.Suppose that A satisfies XAP=0 implies X=0 and XA(I-P)=0 implies X=0.In this paper,we prove thatΦis a nonlinear A^(*)B+B^(*)A type deriva...Let A be a unital^(*)-algebra with the unit I and a nontrivial projection P∈A.Suppose that A satisfies XAP=0 implies X=0 and XA(I-P)=0 implies X=0.In this paper,we prove thatΦis a nonlinear A^(*)B+B^(*)A type derivation on A if and only ifΦis an additive^(*)-derivation.This is then applied to prime^(*)-algebra,von Neumann algebras with no central summands of type I1.factor von Neumann algebras and standard operator algebras.展开更多
基金Supported by the National Natural Science Foundation of China(11601420)the Natural Science Basic Research Plan in Shaanxi Province(2018JM1053)。
文摘Let A be a unital^(*)-algebra with the unit I and a nontrivial projection P∈A.Suppose that A satisfies XAP=0 implies X=0 and XA(I-P)=0 implies X=0.In this paper,we prove thatΦis a nonlinear A^(*)B+B^(*)A type derivation on A if and only ifΦis an additive^(*)-derivation.This is then applied to prime^(*)-algebra,von Neumann algebras with no central summands of type I1.factor von Neumann algebras and standard operator algebras.