φ-半亚正常复合算子的特征

Characteristic of φ Seminormal Composition Operators

设（Ｘ，Σ，ｍ）是完备的σ－有限测度空间，Ｔ是Ｘ→Ｘ的Σ可测映照，则称Ｌ２（Ｘ，Σ，ｍ）上的算子ＣＴ∶ＣＴｆ（ｘ）＝ｆ（Ｔｘ）为复合算子．文中分别给出了ＣＴ是φ－半亚正常算子及完全φ－半亚正常算子的充分必要条件．并解决了Ａ．

Let ( X,Σ,m ) be a complete σ finite measure space, and T be a measurable map from X→X , then the operator C T∶C Tf(x)=f(Tx) on L 2(X,Σ,m) is called a composition operator. The necessary and sufficient conditions for C T to be φ semi hyponormal and absolutely semi hyponormal were given. A solution to the open problem was also provided.