保持Gauss测度的线性算子

Gauss Measures Preserving Linear Operators

设Ｅ是一个复的可Ｂａｎａｃｈ空间，Ｔ是Ｅ上的线性有界算子，若存在Ｅ上的弱稠密序列｛ｘｎ｝，使得在Ｔ下的轨道有界，那么存在关于Ｔ不变的非退化的Ｇａｕｓ测度的充分必要条件是Ｔ的模为１的特征向量全体张成Ｅ．

Let E be a complex separable Banach space,T a linear bounded operator.If there exists a weak- *dense sequence {x * n} in E which have bounded orbits under T *,then the necessary and sufficient conditions for T to accept a nondegenerate invariant Gauss measure is that E is spanned by the unimodular eigenvectors of T.