不变子空间

This paper mainly study the relations between some algebraic properties of Roe algebras and the coarse geometry of metric spaces, and its applications to the reduced crossed product C-algebras and the coarse Baum-Connes conjecture.

本文主要研究这类C~*-代数的某些性质与底空间几何之间的联系及其在交叉积C~*-代数和粗Baum-Connes猜测中的应用。第一章研究交叉积C~*-代数的Schwartz型谱不变子代数。

Li 101 proved the nonlinear ergodic theorem for semitopological semigroups of Lipschitzian mappings in the uniformly convex Banach space with the Frechet differentiable norm without using the concept of invariant mean and submean. In Chapter 1, we extend the results in [23 [24] to the case of almost-orbit.

Li［10］避开了不变平均及不变子平均的概念，在具Frechet可微范数的一致凸Banach空间中，给出了一般拓扑半群上渐近非扩张半群的遍历压缩定理。

Firstly, the recent developments in controllability and observability for switched system are reviewed. Secondly, by means of properties of invariant subspace, the controllability for switched systems with continuous-time and discrete-time subsystems, and a class of discrete impulsive switched systems is respectively investigated. Some sufficient and necessary conditions of controllability are proved. In the end, some simple criterions for controllability and observability of switched symmetric composite systems are set up.

首先介绍了切换系统能控性与能观性方面的一些重要结论；其次，用不变子空间的性质分别研究了同时含有连续子系统和离散子系统的切换系统和一类离散脉冲切换系统的能控性，建立了相应的充分性与必要性判别准则；最后，研究了切换对称组合系统的能控性与能观性，得到了此系统能控性与能观性的简单判据。

In order to investigate the variation of controllability and observability affected by network scheduling,the model of scheduling for Networked Control System is established,which has communication constraint on its input and output channel.Utilizing communication sequence to express the scheduling of channel,the model can be transformed into discrete-time switch system.Under static scheduling,using the theory of recursive invariant subspace and its character,a necessary and sufficient condition of NC...

为了研究网络调度对能控性与能观性的影响，对输入、输出通道都存在通信约束的网络控制系统的调度进行建模；利用通信序列表示通道的调度情况，最终将模型转化为离散切换系统；在静态调度下，利用循环不变子空间理论及其相关的性质，给出了网络控制系统能控性、能观性成立的充要条件，并给出了原有控制系统与经网络静态调度后的系统之间能控性、能观性的关系；最后用仿真实例说明了所提结论的正确性。

This peper is mainly devoted to the study of three kinds of characterizations of simultaneous invariant subspaces, i.e., time domain characterization, frequency domain characterization, and geometric characterization.

摘要本文主要讨论了同时不变子空间的三种特征：即时域特征、频域特征和几何特征。

The cheapest way to get one is to invoke the spectral theorem and to conclude that normal operators always have non-trivial invariant subspaces.

取得这样结果的最省力的尝试是引用光谱定理而得到正规算子恒有非平凡不变子空间的结论。

Especially we completely characterize when two quasi-invariant subspaces are similar or unitarily equivalent.

在相似和〓等价的意义下给出了有限余维的拟不变子空间的完全分类。

For a certain kind of eigenstate controllable system, the convergence of this algorithm can be proved.

对于一类特殊的本征态能控系统(量子控制操作的不变子空间不可约的系统)，该策略可以证明是收敛的。

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。

One of the most important, most difficult, and most exasperating unsolved problem s 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 split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。