Banach space

Banach space的基本解释

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巴拿赫空间

与Banach space相关的网络例句 [注：此内容来源于网络，仅供参考]

In chapter one,the backgrounds and current situation of operator theory in Banach space are introduced and the preliminaries of Banach space are given.In chapter two,we study the existence and uniqueness of fixed point for decreasing strict-set-contraction operator in product space.Under the weak continuous condition,we obtain the existence and uniqueness of fixed point for decreasing operator and we give an application of these results; In chapter three,we get several positive fixed point theorems of decreasing operator and the existence and uniqueness theorems of positive fixed point for operator C=A+B,C=D-A in real Banach space where the order is decided by a normal cone; In chapter four,we obtained some existence and uniqueness theorems of fixed point for some mixed monotone operators in semi-ordered Banach space.

在第一章中，主要介绍了半序Banach空间非线性算子的研究历史背景、现状以及半序Banach空间中的预备知识；在第二章中，我们利用半序方法研究了Banach乘积空间中严格集压缩减算子不动点存在唯一性问题，在弱连续的条件下，得到了不动点的存在唯一性和迭代收敛性，同时，给出了它们的一些应用；在第三章中，我们建立了拟弱连续减算子的正不动点定理，并证明了算子C=A+B，C=D-A的正不动点存在唯一性定理；在第四章中，我们得到了半序Banach空间中混合单调算子的不动点存在性及唯一性定理。

In the first pa.rt,we clolinc the TC inodnhis of convexity and TC modulus of smoothness of quasi-Baiiach space, and prove that the space which is characterized by uniform convexity is same as the space which is cliaracteri/,ed by uniform TC convcxity.Then we give several characterizations of q-uniformly TC convex quasi-Banach space.At the same time ,we prove the triionned-theorcm.In the second part, we give the relationships between some inequalities of martingales with values in quasi-Banach space and uniformly TC convex quasi-Banach space.

本文分四部分，第一部分在拟Banach空间上定义了TC凸性模和TC光滑模并证明了在Banach空间上它分别和一致凸性和一致光滑性刻划的空间是一致的，即Banach空间X是一致TC凸的的充分必要条件是它是一致凸的，Banach空间X是一致TC光滑的充分必要条件是它是一致光滑的，还分别得出了判定一致TC凸和一致TC光滑的几个充分必要条件，同时还证明了在拟范数下的重赋范定理。

Among those; studies, Liu and Bek have obtained many important results for the theory and applications of Banach spaces and their geometry on complex number,(see [3],[41])Here, we have investigated the TP modulus of convexity and TP modulus of smoothness, on the one hand, we have defined a class of new spaces called uniformly TP convex ,on the other hand, we have extended martingale inequalities and the martingale spaces.This article is divided into four parts, in the first part, we define the TP modulus of convexity and TP modulus of smoothness of Banach space, and prove that the space which is characterized by uniform convexity is same as the space which is characterized by TP uniform convexity. Then we give TP q-uniformly convex and TP p-uniformly smoothable characterization of the Banach space. At the same time, we prove the famous renormed theorem.

本文分为四部分，第一部分在Banach空间上定义了一个新的TP凸性模和TP光滑模并证明了在Banach空间上它分别和一致凸性和一致光滑性刻划的空间是同构的，即如果Banach空间X是一致TP凸的充分必要条件是存在一个等价范数，使得在此范数下，它是一致凸的；Banach空间X是一致TP光滑的充分必要条件是存在一个等价范数，使得在此范数下，它是一致光滑的，我们还分别得出了判定一致TP凸和一致TP光滑的一些充分必要条件，同时还证明了箸名的重赋范定理。

与Banach space相关的网络解释 [注：此内容来源于网络，仅供参考]

banach space：巴拿赫空间

在这里,完备的空间有特殊的名称:完备的赋范空间叫巴拿 赫空间(Banach space),完备的内积空间叫希尔伯特空间(Hilbert space). 2. 在有限维空间中空间和它的对偶空间的是完全同构的,而在无限维空间中,它们存 在微妙的差别. 3.

banach space：空间

巴拿赫空间(Banach space)是一种赋有"长度"的线性空间﹐泛函分析研究的基本对象之一. 数学分析各个分支的发展为巴拿赫空间理论的诞生提供了许多丰富而生动的素材. 从外尔斯特拉斯﹐K.(T.W.)以来﹐人们久已十分关心闭区间[a﹐b ]上的连续函数以及它们的一致收敛性.

reflexive banach space：自反巴拿赫空间

reflexive 自反的 | reflexive banach space 自反巴拿赫空间 | reflexive relation 自反关系

bidual banach space：双对偶巴拿赫空间

bidimensionality 二维性 | bidual banach space 双对偶巴拿赫空间 | bifunctor 二变项函子

semiordered banach space：半有序巴拿赫空间

seminorm 半范数 | semiorder 半有序 | semiordered banach space 半有序巴拿赫空间