摘要
设Ｅ是一个复的可分的自反Ｂａｎａｃｈ空间，Ｔ是Ｅ上的有界可逆线性算子．若Ｅ是Ｃｏｔｙｐｅ－２空间，那么Ｔ的模为１的特征向量全体所张成的闭线性子空间等于关于Ｔ的不变的有强二阶矩的Ｂｏｒｅｌ概率测度的支集全体所张成的闭线性子空间．
Let E is a complex separable reflexive Banach space,T is an invertible linear operator on E. If E is a Cotype-2 space,then the closed linear subspace spanned by eigenvetors having norm 1 for T concides with the subspace spanned by the supports of Borel probability measures on E which are invariant under T and have strong second moment.
出处
《山东大学学报（自然科学版）》
CSCD
1995年第2期222-226,共5页
Journal of Shandong University(Natural Science Edition)
关键词
特征向量
不变测度
巴拿赫空间
线性算子
eigenvectors
invariant measure
Cotype-2 space
Gaussian measure
2-absolutely summing operator
eigenoperator
