共查询到20条相似文献,搜索用时 15 毫秒
1.
The purpose of this paper is to provide a random duality theory for the further development of the theory of random conjugate
spaces for random normed modules. First, the complicated stratification structure of a module over the algebra L(μ, K) frequently makes our investigations into random duality theory considerably different from the corresponding ones into classical
duality theory, thus in this paper we have to first begin in overcoming several substantial obstacles to the study of stratification
structure on random locally convex modules. Then, we give the representation theorem of weakly continuous canonical module
homomorphisms, the theorem of existence of random Mackey structure, and the random bipolar theorem with respect to a regular
random duality pair together with some important random compatible invariants. 相似文献
2.
基于概率测度理论基础,研究了随机赋范空间中算子随机范数,得到了线性算子空间与线性泛函的若干随机化结果与随机化的Hahn-Banach延拓定理.结果可能成为随机泛函分析与概率论及应用的理论工具. 相似文献
3.
Tiexin Guo 《Journal of Functional Analysis》2010,258(9):3024-842
The purpose of this paper is to exhibit the relations between some basic results derived from the two kinds of topologies (namely the (ε,λ)-topology and the stronger locally L0-convex topology) for a random locally convex module. First, we give an extremely simple proof of the known Hahn-Banach extension theorem for L0-linear functions as well as its continuous variant. Then we give the relations between the hyperplane separation theorems in [D. Filipovi?, M. Kupper, N. Vogelpoth, Separation and duality in locally L0-convex modules, J. Funct. Anal. 256 (2009) 3996-4029] and a basic strict separation theorem in [T.X. Guo, H.X. Xiao, X.X. Chen, A basic strict separation theorem in random locally convex modules, Nonlinear Anal. 71 (2009) 3794-3804]: in the process we also obtain a very useful fact that a random locally convex module with the countable concatenation property must have the same completeness under the two topologies. As applications of the fact, we prove that most of the previously established principal results of random conjugate spaces of random normed modules under the (ε,λ)-topology are still valid under the locally L0-convex topology, which considerably enriches financial applications of random normed modules. 相似文献
4.
Using the fixed point method, we prove the generalized Ulam-Hyers stability of random homomorphisms in random normed algebras associated with the Cauchy functional equation. 相似文献
5.
Theoretically speaking, there are four kinds of possibilities to define the random conjugate space of a random locally convex module. The purpose of this paper is to prove that among the four kinds there are only two which are universally suitable for the current development of the theory of random conjugate spaces. In this process, we also obtain a somewhat surprising and crucial result: if the base (Ω, F , P ) of a random normed module is nonatomic then the random normed module is a totally disconnected topological space when it is endowed with the locally L0 -convex topology. 相似文献
6.
给出了随机半范模上等度连续的典则模同态族的一个待征——随机半范模上强凸的等度连续的典则模同态族可以被一个性质较好的连续随机半范数所控制. 相似文献
7.
In this paper, we first study the mean ergodicity of random linear operators using some techniques of measure theory and L 0-convex analysis. Then, based on this, we give a characterization for a complete random normed module to be mean ergodic. 相似文献
8.
A Characterization of Continuous Module Homomorphisms on Random Semi—Normed Modules and Its Applications 总被引:1,自引:0,他引:1
TieXinGUO 《数学学报(英文版)》2003,19(1):201-208
In this paper,a characterization of continuous module homomorphisms on random seminormed modules is first given;then the characterization is further used to show that the Hahn-Banach type of extension theorem is still true for continuous module homomorphisms on random semi-normed modules. 相似文献
9.
It is proved that a locally quasi-convex group is a Schwartz group if and only if every continuously convergent filter on its dual group converges locally uniformly. We also show that for metrizable separable groups a similar result remains true when filters are replaced by sequences. As an ingredient in the proofs of these results, we obtain a Schauder-type theorem on compact homomorphisms acting between the natural group analogues of normed spaces. 相似文献
10.
Based on the analysis of stratification structure on random normed modules, we first present random strict convexity and random uniform convexity in random normed modules. Then, we establish their respective relations to classical strict and uniform convexity: in the process some known important results concerning strict convexity and uniform convexity of Lebesgue-Bochner function spaces can be obtained as a special case of our results. Further, we also give their important applications to the theory of random conjugate spaces as well as best approximation. Finally, we conclude this paper with some remarks showing that the study of geometry of random normed modules will also motivate the further study of geometry of probabilistic normed spaces. 相似文献
11.
赵静辉 《数学物理学报(B辑英文版)》1997,(4)
1IntroductionSincetheapproximationaboutpositivelinearoperatorscanbenaturallyinterpretedasthecorrespondingtopicsinprobabilitytheoryswecanuseprobabilitymethodtoconstructorsolvetherelatedproblem([1],[2]).Meanwhile,thetechniquesandidealsusedinapproximationtheorycanbeusedtodealwithsomequestionsinprobabilitytheory,especiallytodiscussthelimittheoryandtoestimatetheconvergentrates.Recently,M.WebastudiedthecentrallimittheorybyusingKorovkintheoryinapproximationtheory([1],[2]).Correspondingtoclassofgene… 相似文献
12.
In this paper, we prove a stability result for the additive Cauchy functional equation in random normed spaces, related to the main theorem from the paper [D. Mihe?, V. Radu, On the stability of the additive Cauchy functional equation in random normed spaces, J. Math. Anal. Appl. 343 (2008) 567–572]. 相似文献
13.
随机自反随机赋范模上的平均遍历定理(英文) 总被引:1,自引:0,他引:1
本文对随机自反随机赋范模上的几乎处处幂有界的随机线性算子证明了一个平均遍历定理,这一定理推广和改进了几个已知的重要的结果. 相似文献
14.
15.
Xiao Lin Zeng 《数学学报(英文版)》2013,29(2):263-280
We first prove various kinds of expressions for modulus of random convexity by using an L~0(F,R)-valued function's intermediate value theorem and the well known Hahn-Banach theorem for almost surely bounded random linear functionals, then establish some basic properties including continuity for modulus of random convexity. In particular, we express the modulus of random convexity of a special random normed module L~0(F,X)derived from a normed space X by the classical modulus of convexity of X. 相似文献
16.
A. Amini-Harandi 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(3):922-926
In this paper, we first give a best approximation theorem in abstract convex metric spaces. As applications, we then derive some best and coupled best approximations and coupled coincidence point results in normed spaces and hyperconvex metric spaces. 相似文献
17.
18.
We consider a problem of Schwaiger in the setting of random normed spaces to obtain a characterization for the completeness of these spaces by means of the stability of the Cauchy additive functional equation. 相似文献
19.
Ioan Goleţ 《Mathematica Slovaca》2007,57(3):259-270
In this paper we consider an enlargement of the notion of the probabilistic normed space. For this new class of probabilistic
normed spaces we give some topological properties. By using properties of the probabilistic norm we prove some differential
and integral properties of functions with values into probabilistic normed spaces. As special cases, results for deterministic
and random functions can be obtained.
相似文献
20.
本文给出了关于L0- 线性函数的Hahn-Banach 扩张定理的几何形式并证明这个几何形式等价于它的代数形式. 进一步, 我们利用这个几何形式给出了随机局部凸模中熟知的基本分离定理的一个新的且简单的证明. 最后, 利用这个分离定理, 我们同时在两种拓扑 —(ε, λ)- 拓扑和局部L0- 凸拓扑下证明了随机赋范模中的Goldstine-Weston 稠密性定理, 并举出一个反例说明在局部L0- 凸拓扑下如果随机赋范模不具有可数连接性质, 则Goldstine-Weston 稠密性定理不一定成立. 相似文献