We introduce the notions of kernel map and kernel set of a bounded linear operator on a Hilbert space relative to a subspace lattice. The characterization of the kernel maps and kernel sets of finite rank operators leads to showing that every norm closed Lie module of a continuous nest algebra is decomposable. The continuity of the nest cannot be lifted, in general.

中文翻译：

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内核映射和运算符分解

我们介绍了希尔伯特空间上相对于子空间格的有界线性算子的核映射和核集的概念。有限秩算子的核映射和核集的表征表明，连续嵌套代数的每个范数闭李模都是可分解的。一般情况下，巢的连续性无法解除。