Lp(S,E,μ)(P≥2)空间上的保测复合算子(英)

Measure Preserving Composition Operators on Lp (S, E,μ) (p≥2)

让(S，E，μ)表示一个可分的概率空间，T是Lp(S，E，μ)的一个复合算子，那么由T的不变测度的支集全体所张成的子空间等于T的单模特征向量全体所张成的子空间．

Let (S,E,μ) denote a separable probability space and T a composition operator on LP (S,E,μ) (p≥2). Then the subspace spanned by the supports of the invariant Borel probability measures for T concides with the subspace spanned by the unimodular eigenvectors of T.