保持算子三乘Jordan积的固定点的映射

Maps Preserving the Fixed Points of Triple Jordan Products of Operators

设B(X)是维数大于等于3的复Banach空间X上有界线性算子全体构成的代数.设A∈B(X),若Ax=x,则称x∈X是算子A的固定点.文章刻画了B(X)上保持算子的三乘Jordan积的固定点的满射.

Let B(X)be the algebra of all bounded linear operators on a complex Banach space X with dim X≥3.For any A∈B(X),x∈X is called a fixed point of A if Ax=x.A characterization of a surjective on B(X)which preserve the fixed points of triple Jordan products of operators is given.