定光桂
主要研究巴拿赫空间上的算子(特别是“等距”算子)与泛函(特别是“拟次加”泛函)理论。
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- 姓名:定光桂
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学术头衔:
博士生导师
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学科领域:
数理逻辑与数学基础
- 研究兴趣:主要研究巴拿赫空间上的算子(特别是“等距”算子)与泛函(特别是“拟次加”泛函)理论。
定光桂 男,回族,1939年生于广西桂林。中共党员。1961年毕业于南开大学。现任南开大学数学系教授(博士生导师),兼任天津市政协常委、科教委员会副主任。1979年在关肇直、吴大任教授推荐下赴瑞典皇家科学院Mittag-Leffler数学研究所进修,由于科研有突出成就,在该所所长,1978-1982届国际数学会主席卡列松教授和著名泛函专家恩福罗教授举荐下,破格获博士学位,成为新中国派往西方学者中第一个获数学博士者。主要研究巴拿赫空间上的算子(特别是“等距”算子)与泛函(特别是“拟次加”泛函)理论,独立发表论文50余篇,出版数学专著4本。1981年回国后(除在美作访问教授和访问学者几年外)一直指导硕、博士生,并在本科及研究生教学第一线工作。从无到有地带出一支有特色,并在国内外有影响的巴拿赫空间理论和泛函分析的学术队伍;有的已在国际学术上享有盛名。由于他在培养研究生及科研上的成就,曾多次获校,天津市的教学和科研奖,特别地,1989年以“培养高质量数学研究生”成果获首届《教学成果优秀奖》国家级奖,1990年因培养少数民族地区年轻数学教师和研究生成绩突出获国家民委《民族团结,进步先进个人奖》。并以科研成果,1991年获国家教委《科技进步奖》,1998年获天津市《科技进步奖》(首届“自然科学奖”)。1999年获天津市“九五”立功奖章。2000年作为“基础数学人才培养基地”成员之一获“天津市特等模范集体”。本人课“泛函分析”获2000年“国家理科基地名牌课程项目”。2001年获“宝钢优秀教师奖”。其所写的专著《巴拿赫空间引论》被(台湾)“九章数学基金会”在其《让数学名著永恒》项目首选为重版书目,并于1997年和1999年由“科学出版社”再版。自1987年来一直承担国家自然科学基金及国家教委博士点基金项目,并任项目负责人。曾任南开大学教务长、数学系主任、天津市数学会副理事长、中国数学会教育委员。连续四届任天津市政协常委至今,并连任两届市政协教育文化委员会及科技教育委员会副主任至今。现为南开大学数学系教授,(由国务院学位委评聘的)博士生导师、国务院“政府特殊津贴”科技人员。并兼任国内一些数学刊物的编委和国外一些著名数学摘刊的特邀评论员。
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定光桂, DING Guanggui
Science in China Ser. A Mathematics 2004 Vol. 47 No.5 722-729,-0001,():
-1年11月30日
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.
isometric mapping,, isometric extension.,
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【期刊论文】L(Ω, μ) CANNOT ISOMETRICALLY CONTAIN SOME THREE-DIMENSIONAL SUBSPACES OF AM-SPACES∗
定光桂, Ding Guanggui
Acta Mathematica Scientia 2007, 27B(2): 225-231,-0001,():
-1年11月30日
This article presents a novel method to prove that: let E be an AM-space and if dim E≥3, then there does not exist any odd subtractive isometric mapping from the unit sphere S(E) into S[L(Ω, μ)]. In particular, there does not exist any real linear isometry from E into L(Ω, μ).
Isometric mapping,, odd and subtractive mapping,, AM-space
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【期刊论文】On the extension of isometries between unit spheres of E and C(Ω) *
定光桂, Guanggui Ding
,-0001,():
-1年11月30日
In this paper, we study the extension of isometries between the unit spheres of ome Banach spaces E and the spaces C(Ω): We obtain that if the set sm:S1(E) of all smooth points of the unit sphere S1(E) is dense in S1(E), then under some condition, every surjective isometry V0 from S1(E) onto S1(C(Ω)) can be extended o be a real linearly isometric map V of E onto C(Ω): From this result we also obtain ome corollaries. This is the first time to study this problem on the differently typical paces, and the method of proof is also very different too.
Extension of isometry,, Smooth point,, WCG,, w-Asplund space
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【期刊论文】A survey on the problems of isometries *
定光桂, Ding Guanggui
,-0001,():
-1年11月30日
In this survey article, we introduce the isometric extension problem of isometric mapping between the unit spheres or open domains also, the distance one preserving problem and some other problems such as the problem of the weak or strong perturbation of linear or nonlinear operators, the problem of the asymptotically isometric operator are also mentioned. Some important results in the development of the related problems are outlined in this paper and some recent advancement and open problems are repointed.
Isometric extension, Isometric approximation, Strong(, weak), almost isometric operator, Asymptotically isometric operator, Distance one preserving mapping
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定光桂, Guanggui Ding
,-0001,():
-1年11月30日
In this paper, we shall present a short and simple proof on the iso-metric linear extension problem of into-isometries between two unit spheres of atomic abstract Lp-spaces (0<p<∞).
isometric extension,, atomic abstract Lp-space
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【期刊论文】The isometric extension problem in the unit spheres of lp(Γ)(p>1) type spaces1
定光桂, Guanggui Ding
,-0001,():
-1年11月30日
In this paper, we first derive the representation theorem of onto isometric mappings in the unit spheres of lp(Γ)(p>1; p 6≠2) type spaces, then we conclude that such mappings can be extended to the whole space as real linear isometries by using the previous result of the author.
Isometric mapping,, strictly convex
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定光桂, problem *, Ding Guanggui
,-0001,():
-1年11月30日
In this paper, we first derived the representation theorem of onto isometric mappings in the unit spheres of l1(Γ) type spaces, then we conclude that such mappings can be extended to the whole space as real linear isometries by using the previous result of the author.
Isometric mapping,, isometric extension
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53浏览
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定光桂, problem *, Ding Guanggui
,-0001,():
-1年11月30日
In this paper, we first derive the representation theorem of onto isometric mappings in the unit spheres of real l1-type spaces, then we conclude that such mappings can be extended to the whole space as (real) linear isometries by using a previous result of the author.
Isometric mapping,, isometric extension
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56浏览
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【期刊论文】On almost isometric embedding from C(Ω) into C0(Ω0) *
定光桂, Ding Guanggui
,-0001,():
-1年11月30日
In this paper we give the suffcient and necessary condition for the existence of any almost isometric operator from C(Ω) into C0(Ω0). As a corollary, we show that there is no∈-isometry from any Abstract M space with a strong unit into C0(Γ) if 0 <∈<9 1
∈-isometry,, isometry,, locally compact,, normal topological space
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【期刊论文】On the boundedness of spheres in F*-spaces *
定光桂, Ding Guanggui
,-0001,():
-1年11月30日
In this paper, some results concerning the relationship between the bound-edness of some spheres and the local boundedness of the F
F*, -space,, sphere,, local boundedness,, compactness
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