ON LINEAR EXTENSION OF 1-LIPSCHITZ MAPPING FROM HILBERT SPACE INTO A NORMED SPACE

In this article, we prove that an into 1-Lipschitz mapping from the unit sphere of a Hilbert space to the unit sphere of an arbitrary normed space, which under some conditions, can be extended to be a linear isometry on the whole space.     

The Representation Theorem of onto Isometric Mappings between Two Unit Spheres of l^1（Γ） Type Spaces and The Application to the Isometric Extension Problem

In this paper, we first derive the representation theorem of onto isometric mappings in the unit spheres of l^1（Γ） type spaces, and then conchlde that such mappings can be extended to the whole space as real linear isometries by using a previous result of the author.     

The representation theorem of onto isometric mappings between two unit spheres of l∞-type spaces and the application on isometric extension problem

In this paper, we first derive the representation theorem of onto isometric mappings in the unit spheres of real l∞-type spaces, then we conclude that such mappings can be extended to the whole space as (real) linear isometries.     

The Isometric Extension of an Into Mapping from the Unit Sphere S（t（2）^∞） to S（L^1（μ））

This is the first paper to consider the isometric extension problem of an into-mapping between the unit spheres of two different types of spaces. We prove that, under some conditions, an into-isometric mapping from the unit sphere S（t（2）^∞） to S（L^1（μ） can be （real） linearly isometrically extended.     

The representation theorem of onto isometric mappings between two unit spheres of l∞-type spaces and the application on isometric extension problem

In this paper, we first derive the representation theorem of onto isometric mappings in the unit spheres of real l∞-type spaces, then we conclude that such mappings can be extended to the whole space as (real) linear isometries.     

THE REALIZATION OF MULTIPLIER HILBERT BIMODULE ON BIDUAL SPACE AND TIETZE EXTENSION THEOREM

51. Introduction and PreliminaryThe multiplier bimodule of imprimitive bimodule and its application to coaction systemwere introduced in [if, but it is generally not an imprimitive bimodule as noted in [II by anexample. In this paper, the same concept is introduced for Hilbert bimodules which properlycontain imprimitive bimodules (for example, the same example as above), and we obtainthe realization of multiplier bimodule on a quotient of bidual space and Tietze extensiontheorem similar to t…     

Extension of isometries between the unit spheres of complex l(Γ)(p>1)spaces

In this paper, we study the extension of isometries between the unit spheres of complex Banach spaces l^p(Γ) and l^p(Δ)(p > 1). We first derive the representation of isometries between the unit spheres of complex Banach spaces l^p(Γ) and l^p(Δ). Then we arrive at a conclusion that any surjective isometry between the unit spheres of complex Banach spaces l^p(Γ)and l^p(Δ) can be extended to be a linear isometry on the whole space.     

On Extension of Isometries Between the Unit Spheres of Normed Space E and lP（p 〉 1）

In this paper, we study the extension of isometries between the unit spheres of normed space E and lP（p 〉 1）. We arrive at a conclusion that any surjective isometry between the unit sphere of normed space lP（p 〉 1） and E can be extended to be a linear isometry on the whole space lP（p 〉 1） under some condition.     

EXTENSION OF ISOMETRIES BETWEEN THE UNIT SPHERES OF COMPLEX lp(Γ)(p > 1) SPACES

In this paper, we study the extension of isometries between the unit spheres of complex Banach spaces lp(Γ) and lp(△)(p 1). We first derive the representation of isometries between the unit spheres of complex Banach spaces lp(Γ) and lp(△). Then we arrive at a conclusion that any surjective isometry between the unit spheres of complex Banach spaces lp(Γ)and lp(△) can be extended to be a linear isometry on the whole space.     

空间l~p(Γ)(1

蒋艳  陈绍雄 《数学学报》2011,(4):687-696

On isometric extension problem between two unit spheres

In this paper we introduce the isometric extension problem of isometric mappings between two unit spheres. Some important results of the related problems are outlined and the recent progress is mentioned.     

关于万有Teichmüller空间T_1的分支

对数导数或pre-SchwaLrz导数组成的万有Teichmtiller空间模型T_1由无限个分支所组成。本文得到了分支L_θ的中心点到有界分支L的距离,同时也对分支L_θ与L的距离及L的中心点到L_θ的距离进行了估计。     

严格凸、光滑、自反的Banach空间中等距映射的线性延拓

本文主要研究了任意两个严格凸,光滑的自反空间E,F的单位球面S(E)和S(F)之间任意等距映射的线性延拓问题.     

等距线性延拓问题

本文引入了两个赋范空间的单位球面间等距映射的延拓问题,并且列出了相关问题的一些重要结果和近期的进展.     

Extension of Isometries Between the Unit Spheres of Normed Space E and C（Ω）

In this paper, we study the extension of isometries between the unit spheres of normed space E and C（Ω）. We obtain that any surjective isometry between the unit spheres of normed space E and C（Ω） can be extended to be a linear isometry on the whole space E and give an affirmative answer to the corresponding Tingley＇s problem （where Ω be a compact metric space）.     

关于β范空间中单位球面间线性等距扩张的一个注记

In this paper, we give four general results on linear extension of isometries between the unit spheres in β-normed spaces. These results improve the corresponding theorems in β-normed spaces.     

拓扑空间到拓扑空间的集值映射的若干定理和等价命题

集值映射已成为数理经济学的一个基本工具,集值映射在经济理论分析中的应用也推动了集值影射本身在数学上的发展.有关集值映射的特性主要建立在欧试空间或度量空间中,这些性质也可以推广到拓扑空间中,但相应的假设较强,其实际应用范围不太理想.本文在主要条件有所减弱的情况下,在拓扑空间中建立集值映射的有关概念和性质,对给出的一些定理进行证明,且得出其他一些结果,如给出极大定理的另一表述和证明.     

赋β-范空间中单位球面上的等距及(λ,κ,2)-等距算子的延拓

通过研究单位球面的几何性质,得到了赋β-范空间的单位球面上的等距算子可以延拓为全空间上的线性等距算子的几个充分条件,然后在赋β-范线性空间中推广了2-等距的概念,定义了(λ,κ,2)-等距和弱(λ,κ,2)-等距,并研究了它们的延拓问题,取得了一些新结果,这些结果是Song M．M．(2003)中的相应结果的推广．     

概率空间上有限测度的维数及其分布

设（Ω，Ｆ，μ）为概率空间，ｖ为（Ω，Ｆ）上的有限测度的密度定理，并研究了ｖ的维数及维数分布的若干性质。     

Henstock-Kurzweil可积函数空间的紧性特征

本文研究Henstock-Kurzweil可积(HK可积)函数空间中的一个经典问题.文章通过研究分布Henstock-Kurzweil积分(DHK积分)的性质,给出了该问题的否定答案.进一步,利用收敛性获得了函数HK可积的一个充分必要条件.最后,在上述结论的基础上刻画了HK可积函数空间的紧性.所得结果丰富和推广了HK可...