保测线性算子的一个注记

A note on preserving linear operator

研究了复的可分Lebesgue空间Lp(S ,∑ ,μ)上保测线性算子的谱性质 ,证明了在 1≤p≤ 2条件下 ,若m是关于T不变的非退化的Gauss测度 ,那么T的旋转特征向量全体张成全空间Lp(S ,∑ ,μ) .

In this note the property of spectrum of measure preserving linear operator T on complex separable Lebesgue space L p(S,∑,μ) is investigated and it is proved that if 1≤ p≤2 and m is invariant nondegenerate Gauss measure for T , then L p(S,∑,μ) is equivalent to the subspace spanned by rotation eigenvectors for T .