Invariant subspaces and unstarred operator algebras.
Invariant subspaces and unstarred operator algebras.
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DOI：
10.2140/pjm.1966.17.511
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发表时间：
1966-06
影响因子：
0.6
通讯作者：
D. Sarason
中科院分区：
文献类型：
--
作者：
D. Sarason
本文证明了：若A是正规Hubert空间算子，且算子B对A的每个不变子空间都保持不变，则B属于由A和恒等式生成的弱闭代数.这可以看作是冯诺依曼双交换子定理的一个改进。给出了一个推广，其中单个算子A被交换的正规算子族所取代。对于A是解析Toeplitz算子的情形，也证明了同样的结果.
It is proved in the present paper that if A is a normal Hubert space operator, and if the operator B leaves invariant every invariant subspace of A, then B belongs to the weakly closed algebra generated by A and the identity. This may be regarded as a refinement of the von Neumann double commutant theorem. A generalization is given in which the single operator A is replaced by a commuting family of normal operators. Also the same result is proved for the case where A is an analytic Toeplitz operator.