It is perhaps worth a short digression to discuss the possibility of the range of an operator not being closed, and its consequences . 在此值得稍离本题讨论算子的值域非闭的可能性及其推论。
In terms of an undefined but self-explanatory phrase, it is just that the compressed operator has the compressed matrix . 用一定未曾定义但意义自明的词组来表示,它正说的是,压缩得到的算子具有压缩得到的矩阵。
One of the most important, most difficult, and most exasperating unsolved problems of operator theory is the problem of invariant subspaces . 算子理论中最重要、最困难也最令人烦恼的未解决问题之一就是不变子空间问题。
The most plausible operatorial generalization of result of preceding paragraph is known as the "mean ergodic theorem for unitary operators. " 前段结果可以推广到算子去,其中最近情近理的推广是“单算子的平均遍历定理”。
Operator theory, like every other part of mathematics, cannot be properly studied without a large stock of concrete examples . 算子理论如同数学的每一其它部分,如果没有大量具体例子作为储备,就不能真正地进行理论考察和研究。