保持一类正规特征值的可加映射

Additive Maps Preserving Parts of Normal Eigenvalues

设B(X)是无限维复Banach空间上全体有界线性算子组成的代数.利用算子谱的性质研究B(X)上双边保持部分正规特征值可加满射的结构,证明该映射是B(X)上的同构或反同构.

Let B(X)be the algebra of all bounded linear operators on an infinite-dimensional complex Banach space.We study the structure of the surjective additive maps on B(X)preserving parts of normal eigenvalues,and prove that the map is either an isomorphism or anti-isomorphism.