| 1. | Every normal operator is trivially subnormal .
每一个正规算子显而易见地是次正规的。 |
| 2. | The least unitary looking contraction operator is 0 .
看来最不象酉算子的压缩算子是0。 |
| 3. | Every contraction can be extended to a partial isometry .
每一压缩算子能被扩张成一个部分等距算子。 |
| 4. | The commutant is one of the most useful things to know about an operator .
换位是关于算子应该知道的最有用的事情之一。 |
| 5. | A process which produces a new function out of any given function is called an operator .
从一个已知函数产生另一个新函数的过程叫做算子。 |
| 6. | 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。 |
| 7. | 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。 |
| 8. | 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。 |
| 9. | 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”。 |
| 10. | 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。 |
