算子的算子点谱的判定

On the Judgement for Operator Point Spectrum of Operator

中文关键词:  亚正常算子  算子点谱

英文关键词:hyponormal operator  operator point spectrum.

中文摘要:

      本文讨论了算子Ａ∈Ｂ（Ｈ）_Ｎ为算子Ｔ∈Ｂ（Ｈ）的算子点谱的判定条件，特别得到：当Ｔ为亚正常算子时，Ａ为Ｔ的算子点谱的判定条件，另外还得到ｋｅｒτ^ｎ_Ｔ，Ａ＝ｋｅｒτ_Ｔ，Ａ成立的充分条件

英文摘要:

      In this paper, we discuss the judgement conditions that A∈B(H)_N is the operator point spectrum of T∈B(H) . In particular, a condition is given for A∈Λ_p(T) when T is a hyponormal operator and A is commutable for T and T^*. Additionally, we obtain the judgement condition forｋｅｒτ^ｎ_Ｔ，Ａ＝ｋｅｒτ_Ｔ，Ａ.