删除或更新信息,请邮件至freekaoyan#163.com(#换成@)

bp(2)空间中的等距映射

本站小编 Free考研考试/2021-12-27

bp(2)空间中的等距映射 王瑞东, 王普天津理工大学理学院 天津 300384 The Isometry on bp(2) Space Rui Dong WANG, Pu WANGDepartment of Mathematics, Tianjin University of Technology, Tianjin 300384, P. R. China
摘要
图/表
参考文献
相关文章

全文: PDF(540 KB) HTML (1 KB)
输出: BibTeX | EndNote (RIS)
摘要度量与线性性质是赋范空间的重要性质,因此,研究线性算子与等距算子的关系成为了泛函分析领域重要的研究课题.本文首先研究一类特殊的赋准范空间,即bp(2)空间的重要性质.然后给出bp(2)空间单位球面间满等距映射的表示定理及延拓性质.
服务
加入引用管理器
E-mail Alert
RSS
收稿日期: 2017-10-23
MR (2010):O177.3
基金资助:国家自然科学基金资助项目(11301384)
作者简介: 王瑞东,E-mail:wangruidong@tjut.edu.cn;王普,E-mail:lubc02@126.com
引用本文:
王瑞东, 王普. bp(2)空间中的等距映射[J]. 数学学报, 2021, 64(1): 155-166. Rui Dong WANG, Pu WANG. The Isometry on bp(2) Space. Acta Mathematica Sinica, Chinese Series, 2021, 64(1): 155-166.
链接本文:
http://www.actamath.com/Jwk_sxxb_cn/CN/ http://www.actamath.com/Jwk_sxxb_cn/CN/Y2021/V64/I1/155


[1] An G. M., Isometries on unit sphere of (Lβn), J. Math. Anal. Appl., 2005, 301:249-254.
[2] Baker J. A., Isometries in normed space, Amer. Math. Monthly, 1971, 78:655-658.
[3] Charzynski Z., Sur les transformationes isométriques des espace du type(F), Studia Math., 1953, 13:94-121.
[4] Cheng L. X., Dong Y. B., On a generalized Mazur-Ulam question:Extension of isometries between unit spheres of Banach spaces, J. Math. Anal. Appl., 2011, 377:464-470.
[5] Diestel J., Geometry of Banach Spaces (Lecture Notes in Mathematics:485), Springer-Berlag, Berlin, 1975.
[6] Ding G. G., On the extension of isometries between unit spheres of E and C(Ω), Acta Math. Sinica, Engl. Ser., 2003, 19(4):793-800.
[7] Ding G. G., The isometric extension of an into mapping from the unit sphere S(l(Γ)) to the unit sphere S(E), Acta Math. Sci. Engl. Ed., 2009, 29B(3):469-479.
[8] Ding G. G., The isometric extension problem in the unit spheres of Lp(Γ) (p > 1) type spaces (in Chinese), Science in China, Ser. A, 2002, 32(11):991-995.
[9] Ding G. G., The representation theorem of onto isometric mapping between two unit sphere of L1(Γ)-type spaces and the application on isometric extension problem, Acta Math. Sinica, Engl. Ser., 2004, 20(6):1089-1094.
[10] Ding G. G., The representation of onto isometric mappings between two spheres of L-type spaces and the application on isometric extension problem, Science in China, Ser. A, 2004, 34(2):157-164(in Chinese); 2004, 47(5):722-729(in English).
[11] Ding G. G., The 1-Lipschitz mapping between the unit spheres of two Hilbert spaces can be extended to a real linear isometry of the whole space, Sci. China Ser. A, 2002, 45(4):479-483.
[12] Ding G. G., New Analysis of Functional Analysis, Science Press, Beijing, 2007.
[13] Fang X. N., Wang J. Y., Extension of isometries between unit spheres of normed space E and l1(Ω), Acta Math. Sinica Chin. Ser., 2008, 51(1):24-28.
[14] Fu X. H., Isometries on the space s, Acta Math. Sci. Ser. B, Engl. Ed., 2006, 26B:502-508.
[15] Gehér G. P., A contribution to the Aleksandrov conservative distance problem in two dimensions, Liacar Algebra Appl., 2015, 481:280-287.
[16] Li J. Z., Isometries on unit spheres of an F -space, Acta Sci. Nat. Univ. Nankai., 2012, 45:80-85.
[17] Liu R., On extension of ismetries between unit spheres of L(Γ)-type space and a Banach space E, J. Math. Anal. Appl., 2007, 333:959-970.
[18] Mankiewicz P., On extension of isoometries in normed linear spaces, Bull. Acad Polon Sci. Ser. Sci. Math. Astronom Phys., 1972, 20:367-371.
[19] Mazur S., Ulam S., Sur less transformationes isometriques d'espaces vectoriels noemes, Comptes Rendus Acad Sci. Paris, 1932, 194:946-948.
[20] Tingley D., Isometries of the unit spheres, Geometriae Dedicata, 1987, 22:371-387.
[21] Wang R. D., On linear Cxtension of isometries between the unit spheres of two-dimensional strictly convex normed space, Acta Math. Sinica Chin. Ser., 2008, 51(5):847-852.
[22] Yi J. J., Wang R. D., Wang X. X., Extension of isometries between the unit spheres of complex lp(Γ) (p > 1) spaces, Acta Math. Sci. Engl. Ed., 2014, 34B(5):1540-1550.
[23] Zhang L., On the isometric extension problem from the unit sphere S(L(2)) into S(L(3)), Acta Sci. Nat. Univ. Nankai., 2006, 39:110-112.

[1]王瑞东, 王普. b(2)空间及b(2)空间上的等距映射[J]. 数学学报, 2019, 62(2): 303-318.
[2]蒋艳, 陈绍雄. 空间lp(Γ)(1 < p < ∞)和Banach空间E的单位球面之间等距算子的延拓[J]. Acta Mathematica Sinica, English Series, 2011, 54(4): 687-696.
[3]谭冬妮;. AL~p-空间单位球面等距算子的延拓的一个注记[J]. Acta Mathematica Sinica, English Series, 2009, (04): 159-162.
[4]王瑞东. 二维严格凸赋范空间单位球面间等距映射的线性延拓[J]. Acta Mathematica Sinica, English Series, 2008, 51(5): 847-852.
[5]方习年;王建华;. 赋范空间E和l~1(Γ)的单位球面间等距映射的延拓[J]. Acta Mathematica Sinica, English Series, 2008, 51(1): 23-28.
[6]侯志彬;张丽娟;. AL~p-空间(1<p<∞)的单位球面间的非满等距映射的延拓[J]. Acta Mathematica Sinica, English Series, 2007, 50(6): 1435-144.
[7]杨秀忠;. 单位球面上的等距及(λ,ψ,2)-等距映射的延拓[J]. Acta Mathematica Sinica, English Series, 2006, 49(6): 1397-140.
[8]王瑞东;. 非满等距映射的线性延拓[J]. Acta Mathematica Sinica, English Series, 2006, 49(6): 1335-133.
[9]钱李新;房艮孙;. 赋以混合范数的各向异性Besov类在不同度量下的嵌入定理[J]. Acta Mathematica Sinica, English Series, 2006, 49(2): 381-390.
[10]方习年;王建华. 单位球面间等距映射的线性延拓[J]. Acta Mathematica Sinica, English Series, 2005, 48(6): -.
[11]杨秀忠;侯志彬;傅小红. 赋β-范空间中单位球面间的等距算子的线性延拓[J]. Acta Mathematica Sinica, English Series, 2005, 48(6): -.
[12]李忠艳;李民丽. C~*-代数的实完全等距映射[J]. Acta Mathematica Sinica, English Series, 2004, 47(1): 67-70.
[13]骆建文;陆芳言. 弱闭T(N)-模的预零化子的等距映射[J]. Acta Mathematica Sinica, English Series, 2003, 46(1): 131-136.
[14]王国俊. 蕴涵格及其Fuzzy拓扑表现定理[J]. Acta Mathematica Sinica, English Series, 1999, 42(1): 133-140.
[15]许连超. 一类非平移算子的平衡态[J]. Acta Mathematica Sinica, English Series, 1991, 34(4): 479-489.



PDF全文下载地址:

http://www.actamath.com/Jwk_sxxb_cn/CN/article/downloadArticleFile.do?attachType=PDF&id=23697
相关话题/空间 数学 理学院 代数 天津理工大学