e/Invariant subspace problem

Information
has gloss	eng: In the field of mathematics known as functional analysis, the invariant subspace problem for a complex Banach space H of dimension > 1 is the question whether every bounded linear operator T : H → H has a non-trivial closed T-invariant subspace (a closed linear subspace W of H which is different from 0} and H such that T(W) ⊆ W).
lexicalization	eng: invariant subspace problem
instance of	e/Unsolved problems in mathematics

Meaning
Chinese
has gloss	zho: 数学领域泛函分析中，最著名的悬而未决的问题之一就是不变子空间问题，有时被乐观地称为不变子空间猜想。这个问题就是如下命题是否成立： :给定一个复希尔伯特空间H，其维度>1，以及一个有界线性算子T : H → H，则H有一个非平凡闭T-不变子空间，也即存在一个H的闭线性子空间W，而且它不同于0}和H，且使得T(W) ⊆ W。
lexicalization	zho: 不变子空间问题