B(X)上保持约当积的固定点的满射

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.Fix(A)表示A的所有固定点的集合.本文刻画了B(X)上保持算子的Jordan积的固定点的满射.     

Bijections preserving invertibility of differences of matrices on <Emphasis Type="Italic">H</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>

We characterise bijections on the space of hermitian matrices preserving the invertibility of differences of matrix pairs in both directions.