| 1. | A linear transformation on milbert space is called compact(also completely continuous) .
希尔伯特空间上的线性变换叫做紧的（也叫全连续的）。 |
| 2. | Lyapunov theorem of operator pairs in hilbert space
希尔伯特空间上算子对的李雅普诺夫定理 |
| 3. | Rigged hilbert space
装备希尔伯特空间 |
| 4. | In appendix a of this paper you find a smooth introduction to rkhs
本文的附录a中，再生核对希尔伯特空间理论有非常贴切的介绍。 |
| 5. | A linear transformation on milbert space is called compact ( also completely continuous )
希尔伯特空间上的线性变换叫做紧的（也叫全连续的） 。 |
| 6. | Aronszajn , n . " theory of reproducing kernels . " trans . amer . math . soc . 686 ( 1950 ) : 337 - 404
这篇文章对核再生希尔伯特空间理论有具体的解说。 |
| 7. | The weyl - moyal transformation takes operator multiplication into the moyal product of functions on the phase space
希尔伯特空间算子乘积与量子空间的函数moyal星乘积之间的关系是由weyl - moyal变换联系起来的。 |
| 8. | Quantum information was originally investigated with the discrete variables ( dv ) and was recently extended to the continuous variables ( cv ) system in the infinite dimension hilbert space
量子信息最早起源于研究单粒子分离变量系统，近期扩展到具有无限维希尔伯特空间的连续变量体系。 |
| 9. | There are two kinds of capacitites depending on the informatoion being transmitted , when we use quantum channel to transmit 0 , 1 seriels we talk about classical capacity , while an unknown quantum state is transmitted , we think of quantum capacity . in the first three chapters , we will concentrated on classical capacities of quantum channels . in chapter 1 an overview is given for the general results of classical capacities of quantum channels as well as a breif introduction to quantum information and basic notations
量子信道的容量有两类；一类是用量子信道传输经典信息，如在光纤上传输0 、 1串，量子态为已知，这时我们谈论经典信息容量，我们将在前三章中讨论，另一类是量子信道传输未知的量子态，这时我们要考虑的是量子信息，是整个希尔伯特空间的传输，其内部的态，纠缠等包含量子相位信息的部分不能被破坏，我们将在后三章中讨论。 |
