关于压缩算子的不变子空间

证明关于压缩算子的如下不变子空间定理：如果T是Hilbert空间H上的压缩算子，且集合Z’={λ∈D；存在z∈H，使得‖z‖=1,且‖（λ-T）z‖＜1/3(1-‖λ‖}是开单位圆D的控制集，那么T有非平凡的不变子空间，这个定理包含了S.Brown,B.Chevreau,C.fPearcy和B.Beauzamy的两个重要结果作为特殊情况，特别是，为个定理包含了S.Brown等人的Hilbert空间上的每个具有厚谱的压缩算子都有平凡的不变子空间这个重要结果作为特殊情况。

On Invariant Subspaces of Contraction Operators

In this paper, we prove a new invariant subspace theorm on contraction operators. that is, if T is a contraction ope rator on the Hilbert space H, and the set Z′=λ∈D; there is z∈H, such that ‖z‖=1, and ‖(λ-T)z‖＜(13)(1-｜λ｜) is dominating in D, where D denotes the interior unit di sc, then T has a nontrivial invariant subsapce. The theorem contains the results of S.Brown, B.Chevreau, C.pearcy and B.Beauzamy as special cases. I n particular, it follows from the theorem that each contraction operator on Hilb ert spaces with rich spectrum has a nontrivial invariant subspace, which was pr oved by S.Brown, B.Chevreau and C.pearch in 1979.