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In this dissertation, we mainly discuss the resonance theorems for families of linear and nonlinear operators, and the theory of bounded linear operator space in F~* spaces.

本文主要研究F~*空间上的线性、非线性算子族的共鸣定理和有界线性算子空间理论。

We show that in error estimates,the condition number 〓 of any invertiblelinear bounded operator T in Banach spaces is minimal.

第III部分考虑条件数在Banach空间中扰动分析的极小性质。

Let 〓 be two Hilbert spaces over the same field,and let T:〓a bounded linear operator with closed range.

在1.4中，我们在最一般条件假设下，给出了Hilbert空间上线性有界算子及其最小二乘解的误差分析，从而完整地解决了Hilbert空间算子的扰动理论。

Let Xand Y be different Banach spaces and 〓Lbe a bounded linear operator,thegeneralized condition number 〓and〓ABA=A,B〓L}are studied.

文章讨论了两类广义条件数的几种表达式，研究了这两类广义条件数之间的关系，并将它们用到算子方程的扰动估计中，推广了Demko[IV.1]中的结果。

In general,the convergent sequence and bounded set are concepts only in topological spaces.

收敛序列和有界集一般是拓扑空间中的概念，文章首先引入序列收敛C和L-空间(给出某种序列收敛关系的向量空间)，然后在其中定义有界集。

This paper investigates the problem of the best weighted simultaneous approximation to totally bounded sequence s from a set G of generalized polynomials with restricted coefficients in complex normed linear spaces X.

在复赋范线性空间X中考察了具限制系数的广义多项式集G对全有界序列的加权同时逼近问题。

It is very interesting to study the boundedness for the commutators related to some integral operator on the functions spaces.

Marcinkiwicz算子作为分析数学中一个重要的积分算子，对它的研究一直是分析数学学者们十分感兴趣的问题。

Montanans like their wide-open spaces, whether they're planted in cities like Missoula or Butte (where the balance of the rugged outdoors with urban conveniences may surprise you), or tucked away in a tiny hamlet like Box Elder or Wise River.

无论蒙大拿人是居住在城市例如：米苏拉或者 Butte （那里的便利的户外活动能让你吃惊），还是住在一个象Box Elder 或者 Wise River那样的小村庄里，他们都喜欢她那广阔的空间。

Visible in the main living spaces as well as along the exterior breezeway, the continuous feature wall lends majestic scale and proportion.

明显的主要居住空间，以及沿线的室外通风道，连续功能墙提供宏伟的规模和比例。

The fragrance, colour and texture of flowers surround and permeate the interior of retail spaces, visually linking them to the roof landscape through the skylights and clerestory windows that bring daylight into the retail arcade.

整个室内的商业空间洋溢着花的芬芳、色彩与感触，通过有自然采光效果的天窗和通风窗将室内景观与屋顶花园在视觉上完美地融合起来。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。