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As an extension, we also obtain some sufficient and necessary conditions under which M_c is left Fredholm and left Weyl for some left invertible operator C, respectively.In chapter 2, the sufficient and necessary condition under which the difference of two idempotent operators on infinite dimensional Hilbert spaces is Fredholm (in-vertible) is discussed. In addition, some equivalent conditions under which products and differences of projections in a C~*-algebra are Moore-Penrose invert-ible are obtained.

来源：Ae5BCab论7a文网www.abclunwen.com对给定的算子对，给出存在左可逆算子C使得M_C左可逆的充要条件；存在可逆算子C使得M_C左可逆的充要条件；存在左可逆算子C使得M_C是左Fredholm算子的充要条件；存在可逆算子C使得M_C是左Fredholm算子的充要条件；存在左可逆算子C使得M_C是左Weyl算子的充要条件；存在可逆算子C使得M_C是左Weyl算子的充要条件。

Three counter-examples of topological space are proposed in this study: There are two metric spaces, X and Y, in which and are isometric, whileand are not isometric; Non-metric tight regular space is a counter-example of the separation of topological space; No non-zero continuous linear functionals of the linear topological space is a counter-example of linear topological space.

这里给出三个反例，存在两个度量空间X与Y，使X^2与Y^2等距而X与Y并不等距是拓扑空间中的反例；存在不可度量化的紧的完全正规空间是拓扑空间分离性的反例；不存在非零连续线性泛函的线性拓扑空间是线性拓扑空间的反例。

Such a problem need us to know whether an onto isometry between the unit spheres of Banach spaces has an linear extension to the whole space?

它是问定义在两个Banach空间单位球面到单位球面上的等距算子是否可以线性等距延拓到整个空间上？

The last section contains the foreign mathematician's work of so called"the asymptotic isometry copy"of classical Banach spaces of c〓, l〓 and l〓. Mainly of the results completed by P.

第五节介绍包含经典Banach空间c〓，l〓和l〓的渐进等距copy问题，主要介绍一些国外学者在这个问题上面所做的工作。

This project also obtained several limit theorems for some important dependent random variables and stochastic processes, such as the Strassen law of the iterated logarithm for negatively dependent random variables, strong limit theorems for mixing random vectors in Banach spaces, sample path properties for two-parameter fractional Wiener processes, and so on.

随机环境中的随机变量与随机过程的研究在国内外相当活跃，本项目主要研究它们的极限性质，着重研究了随机风景中随机变量与随机过程的极限性质，主要取得了以下几个结果：首先对简单对称的Kesten-Spitzer随机游动在低阶矩的条件下给出了强逼近，大大减弱了前人要求任意阶矩的条件，然后对独立风景中的一般随机变量给出了强逼近的一般性结果，由此导出在风景和随机变量都只具有低阶矩的条件下的独立但不同分布、混合相依变量的强逼近，在只有弱高于二阶矩的条件下得到了重相对数律和弱收敛；给出了连续时间参数的Brown风景中Brown运动和稳定风景中稳定过程的滞后增量和连续模等精确样本轨道性质；同时给出了一些重要的相依随机变量和过程的若干极限定理，如负相关随机变量的Strassen重对数律、抽象空间上混合相依变量的一些强极限定理成立的充分必要条件、两参数分数Wiener过程的样本轨道性质等。

Secondly,we develop multiple-dimensional Jacobi polynomial approximations in non-isotropic Hilbert spaces.

本文在建立Jacobi谱方法和拟谱方法数值分析理论的基础上，数值求解这三类问题。

Movements in 3D spaces could only be displayed either jerkily or with minimal details a couple of years ago, but today flowing and quick movements in detailed sceneries are standard features.

几年以前，3D空间内的移动显示极不平稳，细节也不流畅，而时至今日，各种3D场景中的动作流畅而迅速，画面臻于完美，这已经成为3D显示的标准特征。

Avril,your spaces is very jollification.

你的问题还满多的吗，主要是经商啦，这样满意了吧

The juxtaposition of different times and spaces as this work is common in Yin Zhaoyang's works.

这样的错时空并置在尹朝阳的作品中也很常见。

He told Kent the spaces between some of his teeth were too wide.

他告诉肯特，他的一些牙齿之间的缝隙太大。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。