有界线性算子

利用James定理，证明了Banach空间上的有界线性算子的在Wk（X），W（kc）（X）等超空间上的自然扩张映射也是连续的。

Using James theorem , we prove that the natural extension of the bounded linear operator on Banach space is continuous on hyperspace such as W_k ( X ) and W_ ( kc )( X ) .

Gabor框乘子是指能够保持ParsevalGabor框窗口函数的有界线性算子，它有助于分析Gabor框的内部结构，有着重要的理论意义。

A Gabor frame multiplier is a bounded linear operator that preserves the original Parseval Gabor frame window function . It has great theoretical significance as it helps to analyze the inner structure of Gabor frames .

设k∈C（R+）和B是一个有界线性算子。

Let k ∈ C ( R + + ) and B be a linear bounded operator .

W空间中有界线性算子的最佳逼近及其应用

The best approximating of bounded linear operator in the space W and Application

Banach空间有界线性算子加权群逆的存在性

The Existence of W-weighted Group Inverse of Bounded Linear Operators in Banach Spaces

Hilbert空间有界线性算子相似轨道一个定理的证明

Theorem about the similarity orbit closure of linear bonded operator acting of hilbert space

Banach空间中有界线性算子的外逆、内逆存在性的特征

Existence characteristics of inner inverse and outer inverse of bounded linear operators in Banach space

哪样的无穷矩阵能成为可分Hilbert空间上的有界线性算子？

Which infinite matrix can be a bounded linear operator on a separable Hilbert space ?

Hilbert空间H上的有界线性算子K称为紧算子，若K（B1）的闭包（？）

A bounded linear operator K on a Hilbert space H is compact if the image of the unit ball of H under K has compact closure .

本文以自然的方式定义了从Z-空间X到Z-空间Y的有界线性算子的和以及它们的数乘.从而得到了与赋范空间的对偶空间理论类似的一系列结论。

Bounded linear operators from one Z-space X to another Y are defined naturally , and some results which approximates to the dual spaces theory of normed spaces are obtained .

A：X→Y是零指标Fredholm有界线性算子。

A : X → Y is bounded linear Fredholm operator with zero index .

本文证明了可分无穷维Hilbert空间上每个有界线性算子均可写成两个强不可约算子之和。

In this paper , we prove that every operator on a separable , infinite dimensional Hilbert space is the sum of two strongly irreducible operators .

本文讨论了Banach空间中有界线性算子的有界外逆的扰动，给出了外逆的表示形式以及扰动的上界。

In this paper , we discuss the perturbation of bounded outer-inverse of bounded linear operators in Banach space and obtain some new upper bounded of perturbation .

证明了：（1）若A可交换或A为一有限维的C-代数时，Δ可以延拓成为AA到A的一个有界线性算子；

We prove that if Ais a finite dimensional C - algebra , then Δ can be extended to be a bounded linear operator from A Ato A .

第3节证明Hilbert空间上每个有界线性算子都可以用完全不可约算子的有限直接和来逼近。

In section 3 it is proved that every bounded linear operator on Hilbert space can be approximated by the finite direct sum of completely irreducible operators .

如果Hilbert空间上一个有界线性算子的谱的凸壳等于数值城的闭包，则它称为凸型算子。

A bounded linear operator on a Hilbert space is said to be convexoid , if the convex hull of its spectrum is equal to the closure of its numerical range .

本文讨论了有限维Hilbert空间中有界线性算子的最佳广义逆问题，证明了Moore-Penrose广义逆为最佳的。

We discuss the best generalized inverse of linear bounded operator in finite dimension Hilbert space . We proved Moore - Penrose generalized inverse is the best generalized inverse .

泛函分析学中的有界线性算子定理，Hahn-Banach定理以及共鸣定理都可以移植于次范整线性空间之中。

Analogues the bounded linear operator theorem , the Hahn-Banach theorem and the resonance theorem are established in sub-normed Z-linear space .

该文研究Lipschitz映射空间作为一个Banach空间的结构性质，主要研究了它的闭子空间有界线性算子空间（赋予算子范数）在其中的可余性。

In this paper we study the structures properties of the space of Lipschitz mappings as a Banach spaces , mainly we have studied the complementarity of its closed subspace the space of bounded linear operators .

研究了Banach空间中的一个等价性质，证明了Banach空间中Radon-Nikodym性质在一定条件下可以导出有界线性算子的可表示性。

We study an equivalent property in Banach space and it is proved that under certain conditions the representability of a linear operator in Banach space can be derived by the Radon-Nikodym property .

给出了定向偏序群上Hankel算子的定义，得到了一个有界线性算子为Hankel算子的充要条件。

In this paper , Hankel operators on directed partially ordered groups are defined . A necessary and sufficient condition is given under which a bounded linear operator becomes a Hankel operator .

第一节我们介绍了vonNeumann代数，因子vonNeumann代数，子空间格，套代数及有界线性算子等概念。

In section I , we give some technologies and notations , and introduce the definitions of von Neumann algebras , factor von Neumann algebras , subspace lattices , nest algebras and bounded linear operators and so on .

设T是复的可分的自反Banach空间X上的幂有界线性算子，若在X上存在关于T不变的非退化可积Borel概率测度m，那么T旋转特征向量全体张成X。

Let T be a power bounded linear operator on a compler seperable and reflexive Banach space X if there exists a invariant nondegenerate and integrable Borel probability measure on X for T , then X is spanned by eigenvectors of T with unimodular eigenvalue .

本文在包含可补子空间同构于C0或l1的Banach空间上构造了一个B型良性有界线性算子，但其共轭算子不是B型的。

In this paper , we structure a linear operator T on Banach space X which contains a complemented subspace isomorphic to C0 or l1 . T is well-bounded of type ( B ), but T is not .

在这种空间上：证明有界线性算子T的谱σ（T）有特殊性，例如，谱σ（T）中存在唯一点λT使T&λTI是非本性算子；

On such spaces : it is shown that the spectrum σ( T ) of a bounded linear operator T has some special properties , for instance , there is an unique point λ _T in σ( T ) such that T - λ tI is an inessential operator ;

然后利用有界线性算子半群的理论，证明了由闭环系统所确定的算子是预解紧的耗散算子，生成C0压缩半群，从而得到了系统的适定性。

Then it shows that the operator determined by the system is dissipative and generates a C0 semigroup , and hence the well-posed-ness of the system follows from the semigroup theory of bounded linear operators .

本文讨论了一类具有垂直传染的年龄结构SEIR流行病模型，运用有界线性算子半群理论证明了模型本身非负解的存在唯一性。

This paper discusses an age-structured SEIR epidemic model with vertical trans - mission . The existence and uniqueness of nonnegative solution to the model are proved by using the theory of bounded linear operator semigroup ;

本文将Banach空间上两两可交换的有界线性算子组的Taylor联合谱的定义推广到含有一个闭算子的算子组的情况，并证明了这种算子组的谱是C~n中的一个闭集。

Here , the definition of Taylor joint spectrum of tuple of commuting bounded linear operators on Banach spaces is extended to the case when the tuple includes a closed operator . Also , the spectrum of this tuple is proved to be a closed set in C ~ n.

再生核空间的有界线性算子的最佳逼近

Best Approaching of Bounded Linear Operator in Reproducing Kernel Space

两个有界线性算子的联合数值域

The Joint Numerical Range of Two Bounded Linear Operators