幂有界共轭线性算子的不变测度

Invariant measures for power bounded conjugate linear operators

设T是复的可分的自反Banach空间X上的幂有界线性算子 ,若在X 上存在关于T 不变的非退化可积Borel概率测度m ,那么T旋转特征向量全体张成X .

Let T be a power bounded linear operator on a compler seperable and reflexive Banach space X if there exists a invariant nondegenerate and integrable Borel probability measure on X * for T, then X is spanned by eigenvectors of T with unimodular eigenvalue.