关于Hilbert空间的不变子空间问题

On the Invariant Subspace in Hilbert Space

有界线性算子在无穷维可分复Hilbert空间上的不变子空间问题至今仍是一个未解难题。通过引进该Hilbert空间的一组正交基,在该组正交基满足一定的条件下,有界线性算子在该Hilbert空间上一定有一个非平凡的不变子空间。

It is still an unsolved problem that whether every bounded linear operator on an infinite-dimensional separable eomplex Hilbert spaee has a nontrivial invariant subspaee. By introdueing a set of orthogonal basis in the Hilbert space, this paper proves that if the orthogonal base met eertain eonditions, the eorresponding bounded linear operator must have a nontrivial invariant subspaee in the Hilbert spaee.