L_p(p≥2)空间上复合算子的不变测度

INVARLANT MEASURES FOR COMPOSITION OPERATORS ON L p(p≥2)

设（Ｓ，Σ，μ）是一个可分的概率空间，Ｔ是Ｌｐ（Ｓ，Σ，μ）上的复合算子。

Let T be a composition operator induced on Lebesgue spaces L p(S,Σ,μ)(p≥2)by Tf(·)=f(h(·))where h:S→S is a nonsingular transformation.Then the subspace spanned by the supports of the invariant Borel probability measure for T concides with the subspace spanned by the unimodular eigenvectors of T.