A Characterization of Continuous Module Homomorphisms on Random Semi—Normed Modules and Its Applications 被引量：12

A Characterization of Continuous Module Homomorphisms on Random Semi-Normed Modules and Its Applications

导出

摘要 In this paper, a characterization of continuous module homomorphisms on random semi-normed 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. In this paper, a characterization of continuous module homomorphisms on random semi-normed 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.

作者 TieXinGUO

机构地区 DepartmentofMathematics

出处《Acta Mathematica Sinica,English Series》 SCIE CSCD 2003年第1期201-208,共8页 数学学报（英文版）

关键词 Random semi normed modules Continuous module homomorphisms Extension theorems Random semi normed modules Continuous module homomorphisms Extension theorems

分类号 O177.5 [理学—基础数学]

引文网络
相关文献

参考文献5

1郭铁信.随机度量理论及其应用在我国最近进展的综述(英文)[J].应用泛函分析学报,2001,3(2):129-158. 被引量：14
2郭铁信.关于随机赋范空间与随机内积空间的某些基本理论(英文)[J].应用泛函分析学报,1999,1(2):160-184. 被引量：40
3郭铁信.Representation theorems of the dual of Lebesgue-Bochner function spaces[J].Science China Mathematics,2000,43(3):234-243. 被引量：8
4郭铁信.Radon-Nikodym property of conjugate Banach spaces and w*-equivalence theorems of w*-u-measurable functions[J].Science China Mathematics,1996,39(10):1034-1041. 被引量：11
5郭铁信.随机度量理论及其应用在我国最近进展的综述(英文)[J].应用泛函分析学报,2001,3(3):229-230. 被引量：23

二级参考文献31

1巩馥洲.完备赋准范空间上一类无界线性随机算子的谱分解定理[J].数学进展,1994,23(5):432-438. 被引量：1
2游兆永,朱林户.随机共轭空间与随机对偶[J].工程数学学报,1996,13(A12):77-89. 被引量：1
3C. Alsina,B. Schweizer,A. Sklar.On the definition of a probabilistic normed space[J]. Aequationes Mathematicae . 1993 (1-2)
4R. M. Dudley,Walter Philipp.Invariance principles for sums of Banach space valued random elements and empirical processes[J]. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete . 1983 (4)
5H. Sherwood.Complete probabilistic metric spaces[J]. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete . 1971 (2)
6Bharucha-Reid A T.Fixed point theorems in probabilistic analysis. Bulletin of the American Mathematical Society . 1976
7LIU Qing-rong,GONG Fu-zhou.The orthodecomposition theorem in a class of random inner product spaces andits applicatons. Chinese Annals of Mathematics . 1992
8LIN Xi,LI Chuan-mu.Orthoprojection theorems in random inner product spaces. Chinese J of Engg Math . 1991
9Serstnev A N.Random normed spaces:problems of completeness. Kazan Gos. Unly. Ucen. Zap . 1962
10YOU Zhao-yong,GUO Tie-xin.Pointwise best approximation in the space of strongly measurable functions withapplications to best approximation in L~P(μ, X). Journal of Approximation Theory . 1994

共引文献44

1杨玉洁.完备随机赋范模中的Drop定理与Petal定理[J].应用泛函分析学报,2012,14(4):411-418.
2GUO TieXin,CHEN XinXiang.Random duality[J].Science China Mathematics,2009,52(10):2084-2098. 被引量：3
3GUO TieXin Key Laboratory of Information Mathematics and Behavior of Ministry of Education, Department of Mathemat-ics, Beihang University, Beijing 100083, China.The relation of Banach-Alaoglu theorem and Banach-Bourbaki-Kakutani-mulian theorem in complete random normed modules to stratification structure[J].Science China Mathematics,2008,51(9):1651-1663. 被引量：18
4张志明.随机内积空间中的不动点定理和变分不等式[J].云南师范大学学报（自然科学版）,2004,24(5):8-9. 被引量：3
5孟红,王卫,刘露.Part II　Example Cases[J].World Journal of Acupuncture-Moxibustion,2000,10(2):63-64.
6郭铁信,孟永森.完备随机内积模上稠定模同态的共轭算子[J].数学研究,2005,38(4):367-372.
7易文德,王沁.两类特殊的联系函数(Copula)[J].数学研究,2005,38(4):428-433.
8赵登虎.关于随机赋范模中最佳逼近的一个注记[J].大学数学,2005,21(6):95-99.
9郭铁信,李克华.完备随机内积模上的Hellinger-Toeplistz定理[J].厦门大学学报（自然科学版）,2006,45(1):23-25.
10郭铁信,倪丹.完备随机内积模中的Friedrichs定理[J].厦门大学学报（自然科学版）,2006,45(1):26-28.

同被引文献27

1SONG Yongsheng YAN Jia'an.The representations of two types of functionals on L^∞(Ω,F) and L^∞(Ω,F,P)[J].Science China Mathematics,2006,49(10):1376-1382. 被引量：5
2GUO TieXin,CHEN XinXiang.Random duality[J].Science China Mathematics,2009,52(10):2084-2098. 被引量：3
3SONG YongSheng,YAN JiaAn.An overview of representation theorems for static risk measures[J].Science China Mathematics,2009,52(7):1412-1422. 被引量：2
4GUO TieXin Key Laboratory of Information Mathematics and Behavior of Ministry of Education, Department of Mathemat-ics, Beihang University, Beijing 100083, China.The relation of Banach-Alaoglu theorem and Banach-Bourbaki-Kakutani-mulian theorem in complete random normed modules to stratification structure[J].Science China Mathematics,2008,51(9):1651-1663. 被引量：18
5郭铁信,游兆永.随机内积模上的Riesz表示定理及其应用[J].数学年刊（A辑）,1996,1(3):361-364. 被引量：13
6郭铁信.共轭空间的Radon-Nikodym性质及其中弱-u-可测函数的弱-等价性定理[J].中国科学（A辑）,1996,26(7):604-610. 被引量：6
7郭铁信.随机对偶空间[J].厦门大学学报（自然科学版）,1997,36(2):167-170. 被引量：5
8郭铁信.随机赋范模为随机自反的特征[J].厦门大学学报（自然科学版）,1997,36(4):499-502. 被引量：6
9郭铁信,曾小林.随机赋范模上非零连续线性泛函的存在性[J].工程数学学报,2008,25(1):117-123. 被引量：4
10Tie-xin GUO Department of Mathematics, School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083, China.Several applications of the theory of random conjugate spaces to measurability problems[J].Science China Mathematics,2007,50(5):737-747. 被引量：4

引证文献12

1GUO TieXin,CHEN XinXiang.Random duality[J].Science China Mathematics,2009,52(10):2084-2098. 被引量：3
2郭铁信.随机度量理论的最近进展及其应用[J].工程数学学报,2004,21(F12):135-144. 被引量：4
3郭铁信,曾小林.随机赋范模上非零连续线性泛函的存在性[J].工程数学学报,2008,25(1):117-123. 被引量：4
4陈新香,郭铁信.关于随机对偶性的一个注记[J].数学研究,2009,42(4):383-388.
5GUO TieXin.Recent progress in random metric theory and its applications to conditional risk measures[J].Science China Mathematics,2011,54(4):633-660. 被引量：18
6赵世恩,石光.L^0-线性函数的Hahn-Banach扩张定理的几何形式与随机赋范模中的Goldstine-Weston定理[J].中国科学：数学,2011,41(9):827-836. 被引量：1
7赵世恩.关于随机最远点(英文)[J].应用泛函分析学报,2011,13(4):351-356.
8Tie Xin GUO,Shi En ZHAO.On the Random Conjugate Spaces of a Random Locally Convex Module[J].Acta Mathematica Sinica,English Series,2012,28(4):687-696. 被引量：3
9汤约翰.完备随机赋范代数中的Gleason-Kahane-Zelazko定理(英文)[J].应用泛函分析学报,2012,14(1):40-45.
10郭铁信,赵世恩,曾小林.随机凸分析(Ⅰ):随机局部凸模中的分离性以及Fenchel-Moreau对偶性[J].中国科学：数学,2015,45(12):1961-1980. 被引量：2

二级引证文献27

1杨玉洁.完备随机赋范模中的Drop定理与Petal定理[J].应用泛函分析学报,2012,14(4):411-418.
2GUO TieXin,CHEN XinXiang.Random duality[J].Science China Mathematics,2009,52(10):2084-2098. 被引量：3
3郭培华,林荣辉,黄建华.关于随机内积模上强非线性拟变分不等式及补问题[J].福州大学学报（自然科学版）,2007,35(5):654-657.
4郭培华,黄建华.随机内积模上广义强非线性拟变分不等式[J].云南师范大学学报（自然科学版）,2007,27(6):10-14.
5郭进利.概率度量空间在分形图理论中的应用[J].纯粹数学与应用数学,2008,24(2):292-300.
6陈新香,郭铁信.关于随机对偶性的一个注记[J].数学研究,2009,42(4):383-388.
7GUO TieXin.Recent progress in random metric theory and its applications to conditional risk measures[J].Science China Mathematics,2011,54(4):633-660. 被引量：18
8赵世恩,石光.L^0-线性函数的Hahn-Banach扩张定理的几何形式与随机赋范模中的Goldstine-Weston定理[J].中国科学：数学,2011,41(9):827-836. 被引量：1
9赵世恩.关于随机最远点(英文)[J].应用泛函分析学报,2011,13(4):351-356.
10张霞,郭铁信.随机自反随机赋范模上的平均遍历定理(英文)[J].数学进展,2012,41(1):21-30. 被引量：1

1丁争尚,郭健.关于线性泛函的一个延拓定理[J].纺织高校基础科学学报,2001,14(1):45-47.
2李德荣.科学家的故事——哈恩发现核裂变[J].物理教学探讨（初三年级学研期）,2003(14):19-19.
3肖泽昌.Exact Sequence and Commutative Diagrams of Semimodule Homomorphism[J].Chinese Quarterly Journal of Mathematics,1997,12(2):108-110. 被引量：1
4俞鑫泰,王嘉平.关于基的Hahn—Banach延拓[J].华东师范大学学报（自然科学版）,1989(3):29-33.
5费米实验室的加速器[J].大科技（科学之谜）（A）,2017,0(3):32-33.
6Tongke Wang.Alternating Direction Finite Volume Element Methods for Three-Dimensional Parabolic Equations[J].Numerical Mathematics(Theory,Methods and Applications),2010,3(4):499-522. 被引量：1
7Zhang, LC,Ma, JP.Free C *- algebras and the problem of uniqueness of extension in non-commutative Hahn-Banach Theorem[J].Chinese Science Bulletin,1997,42(13):1076-1079.
8何穗.弱Hahn-Banach光滑Banach空间的一个特征性质(英文)[J].华中师范大学学报（自然科学版）,1990,24(1):19-21.
9李国祯.几个随机算子定理[J].应用泛函分析学报,2004,6(4):351-357. 被引量：1
10盛宝怀,刘三阳,毛华.THE EXTENSION THEOREMS OF CONE LINEAR OPERATORS[J].Applied Mathematics and Mechanics(English Edition),2002,23(1):71-78.

Acta Mathematica Sinica,English Series

2003年第1期

浏览历史

内容加载中请稍等...