准齐性算子族的共鸣定理

本文给出了值域空间为有序拓扑向量空间的准齐性算子族的几个共鸣定理.     

准齐性算子族的共鸣定理

本文给出了值域空间为有序拓扑向量空间的准齐性算子族的几个共鸣定理.     

模糊赋范线性空间中准齐性算子族的等度连续性

在模糊赋范线性空间中研究点态模糊有界的准齐性算子族的等度连续性, 并且建立点态模糊半有界与点态非模糊无界的准齐性算子族的共鸣定理.作为其推论, 得到了经典的赋范线性空间和Menger概率赋范线性空间中相应的结论.     

随机赋范空间中算子随机范数与共鸣定理及应用

基于概率论理论基础,给出了随机赋范空间中算子的随机范数定义,在此基础上,应用逆算子定理证明了随机赋范空间中算子族的共鸣定理,它以Banach空间中的共鸣定理为特例,是Banach空间中的共鸣定理的随机化形式,随机化的共鸣定理刻划了在随机赋范空间框架下随机变量族的一致有界性.随机赋范空间中的共鸣定理将可能成为随机泛函分析与概率论的新应用工具.     

F*空间上点态半有界和非无界线性算子族的共鸣定理

证明每个F~*空间(即满足第一可数公理的Hausdorff拓扑向量空间)可借助于它的"标准生成伪范数族"来表征.利用标准生成伪范数族P,在F~*空间中引入P-有界集、P-半有界集和P-无界集的概念,建立点态半有界和非无界线性算子族的共鸣定理.作为其推论,得到了Menger概率赋范空间中点态概率半有界和非概率无界线性算子族的共鸣定理,改进并推广了某些已有的结果.     

完备赋准空间上一类无界线性随机算子的谱分解定理

本文利用随机内积空间方法给出了完备赋准空间上一类无界线性随机算子的谱分解定理。引结果不仅推广了对称随机线性算子的谱分解定理，而且限于原情形也使其处理简明、清晰。     

完备赋准范空间上一类无界线性随机算子的谱分解定理

本文利用随机内积空间方法给出了完备赋准范空间上一类无界线性随机算子的谱分解定理。此结果不仅推广了对称随机线性算子的谱分解定理，而且限于原情形也使其处理简明、清晰。     

FTL—空间上的Fuzzy连续线性算子

本文将[1]中给出的fuzzy线性算子的定义作了适当的修改,使之更适合于在fuzzy拓扑线性空间(简称FTL-空间)中研究。我们证明了fuzzy线性算子的一个分解定理。在此基础上,研究了FTL-空间上fuzzy线性算子的连续性的一系列等价刻划,讨论了fuzzy线性算子的连续性与有界性的关系。最后,给出了FTL-空间上fuzzy连续线性算子族的一致有界原理。     

Mazur-Ulam定理的一个注记

本文的主要结论是给出了一个更广泛形式的Mazur-Ulam定理.讨论的对象是实的赋准范空间,满等距算子被减弱成其像空间构成一个加法子群的算子.最后给出的推论推广了Skof的一个结果.     

赋准范空间之间线性算子的五种有界性与连续性

综合散见于多种文献的不同描述,明确线性算子拓扑有界、邻域有界、范有界与强有界的定义,引进次强有界的概念,给出赋准范空间之间与赋β-范空间之间线性算子的各种有界性以及连续性之间的关系定理与反例.     

Operators associated with the Jacobi semigroup

The aim of this paper is to introduce some operators induced by the Jacobi differential operator and associated with the Jacobi semigroup, where the Jacobi measure is considered in the multidimensional case.In this context, we introduce potential operators, fractional integrals, fractional derivates, Bessel potentials and give a version of Carleson measures.We establish a version of Meyer’s multiplier theorem and by means of this theorem, we study fractional integrals and fractional derivates.Potential spaces related to Jacobi expansions are introduced and using fractional derivates, we give a characterization of these spaces. A version of Calderon’s Reproduction Formula and a version of Fefferman’s theorem are given.Finally, we present a definition of Triebel–Lizorkin spaces and Besov spaces in the Jacobi setting.     

Lax定理与连续左逆的存在性

本文在局部凸空间的框架下,研究了一般线性算子（未必连续）存在连续左逆的条件,从而获得了Lax定理的一系列新的推广.     

Characterizations of Some Matrix Classes of Quasi-Homogeneous Operators

In this paper, we give a general characterization of a class of matrices of quasi-homogeneous operators between topological vector spaces.     

A uniform boundedness theorem for locally convex cones

We prove a uniform boundedness theorem for families of linear operators on ordered cones. Using the concept of locally convex cones we introduce the notions of barreled cones and of weak cone-completeness. Our main result, though no straightforward generalization of the classical case, implies the Uniform Boundedness Theorem for Fréchet spaces.

     

关于sn可度量空间的注记

具有σ局部有限sn网的空间称为sn可度量空间.本文利用紧覆盖映射、点星网、CF族的概念,给出了sn可度量空间的新刻画.     

Locally conformally homogeneous pseudo-Riemannian spaces

Locally homogeneous Riemannian spaces were studied in [1–4]. Locally conformally homogeneous Riemannian spaces were considered in [10]. Moreover, the theorem claiming that every such space is either conformally flat or conformally equivalent to a locally homogeneous Riemannian space was proved.In this article, we study locally conformally homogeneous pseudo-Riemannian spaces and prove a theorem on their structure. Using three-dimensional Lie groups and the six-dimensional Heisenberg group [11], we construct some examples showing the difference between the Riemannian and pseudo-Riemannian cases for such spaces.     

Adjoint for operators in Banach spaces

In this paper we show that a result of Gross and Kuelbs, used to study Gaussian measures on Banach spaces, makes it possible to construct an adjoint for operators on separable Banach spaces. This result is used to extend well-known theorems of von Neumann and Lax. We also partially solve an open problem on the existence of a Markushevich basis with unit norm and prove that all closed densely defined linear operators on a separable Banach space can be approximated by bounded operators. This last result extends a theorem of Kaufman for Hilbert spaces and allows us to define a new metric for closed densely defined linear operators on Banach spaces. As an application, we obtain a generalization of the Yosida approximator for semigroups of operators.

     

Pontriagin空间上算子的交换性

证明了:当Pontrjagin空间上的正规算子A没有零性不变子空间时,Putnam- Fuglede定理成立;当正规算子A有零性不变子空问时,通过构造反例说明此时Putnam- Fuglede定理不成立,并对Π1空间上算子相关的交换性条件进行了讨论,得到了Π1空间上算子代数的二次交换定理．     

Besov 空间上的算子插值定理

本文研究了算子的插值问题.利用Riesz-Thorin定理的证明方法,并运用Daubechies小波得到了Besov空间上的线性算子的插值定理.