摘要
研究了C_p(1≤p<+∞)中的相似不变子空间和C_p(1≤p<+∞)上的双边保相似线性映射。利用相似轨道理论,证明了C_1中有唯一的非平凡相似不变子空间,C_p(1<p<+∞)中没有非平凡相似不变子空间。同时给出了C_p(1≤p<+∞)上的双边保相似线性映射的表示。
Similarity—invariant subspaces in C_p and the bounded linear maps on C_p which preserve similarity in both directions are studied. With the theory of similarity orbits, it is proved that there is only one nontrivial similarity invariant subspace in C_1, and no nontrivial similarity invariant subspace in C_p(1<p<∞), At the same time, the representations of bounded linear maps which prserve similarity in both directions are given.
出处
《陕西师大学报（自然科学版）》
CSCD
1993年第4期4-7,共4页
Journal of Shaanxi Normal University(Natural Science Edition)
关键词
线性算子
不变子空间
线性映射
linear operator
similarity orbit
invariant subspace
similarity—preserving linear map
