矩阵环Mn(C)上的广义Jordan*-导子

Generalized Jordan……*-derivations of matrix ring Mn(C)

研究了矩阵环Mn(C)上满足条件D(x^2)=D(x)x^*+xD(x),x∈Rn或x∈Sn的广义Jordan^*-导子,其中,Rn和Sn分别是严格上三角矩阵的集合和上三角矩阵的集合。Rn确定的广义Jordan^*-导子不是平凡的,Sn确定的广义Jordan^*-导子是零导子。此外,还确定了满足D(x)=-xD(x^-1)x^*,x为可逆矩阵条件下的广义Jordan^*-导子都是零导子。

We study the generalized Jordan*-derivations of matrix ring Mn(C)determined by D(x^2)=D(x)x^*+xD(x),x∈Rn or x∈Sn,where Rn and Sn are the sets of strictly upper triangular and upper triangular matrices,respectively.The generalized Jordan*-derivations determined by Rn are nontrivial,and the generalized Jordan*-derivations determined by Sn are zero derivations.In addition,if the generalized Jordan*-derivations satisfy the condition D(x)=-xD(x-1)x^*for the invertible matrix x∈Mn(C),then they are zero derivations.