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Hilbert空间中稠定闭线性算子的Moore-Penrose正交广义逆的扰动
  • ISSN号：1000-0984
  • 期刊名称：《数学的实践与认识》
  • 时间：0
  • 分类：O177[理学—数学;理学—基础数学]
  • 作者机构：[1]浙江交通职业技术学院管理与信息系, [2]南京大学数学系
  • 相关基金：Supported by NNSF of China(10671049,10771101)
作者： 陈静仁[1], 王玉文[1], 刘萍[1]
关键词： GRASSMANN流形, 微分结构, 无穷维Grassmann流形, Grassmann manifold, Infinite dimensional Grassmann manifold, Differentiable structure
中文摘要：

设E是Banach空间,G(E)表示空间E中可分裂的子空间全体,和U(N)={HE:H  N=E}.让F∈U(N).1983年,Abraham,Marsden和Ratiu给出G(E)上的一个微分结构{(U(N),Ψ_(F,N)}_(N∈G(E)),使得G(E)成为光滑Banach流形.然而即使在1988年他们的第二版书中,粘贴映射Ψ_(F,N) oΨ_(F_1,N_1)~(-1)光滑性的证明有洞,仍未成功.在这篇小文里,这个洞被指出,并给出了一个新的证明.这样,光滑无穷维Grassmann流形G(E)完全被证明.

英文摘要：

Let E be a Banach space,G(E) the set of all split subspaces in E,and U(N)={H E:H N = E}.In 1983,Abraham,Marsden and Ratiu first proposed a differentiable structure on G(E),{(U(N),ψ_(F,N))}_(N∈G(E)) where F  N = E.It makes G(E) become a infinite dimensional and smooth Banach manifold.As we know,for the projective spaces RP~n and CP~n,the smooth infinite dimensional manifold G(E) will play an important role in the study of infinite dimensional geometry.However,even in 1988,the proof of the smooth overlap m...

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期刊信息
  • 《数学的实践与认识》
  • 中国科技核心期刊
  • 主管单位:中国科学院
  • 主办单位:中国科学院数学与系统科学研究院
  • 主编：林群
  • 地址：北京大学数学科学学院
  • 邮编：100871
  • 邮箱：bjmath@math.pku.edu.cn
  • 电话：010-62759981
  • 国际标准刊号：ISSN：1000-0984
  • 国内统一刊号：ISSN：11-2018/O1
  • 邮发代号:2-809
  • 获奖情况:
  • 国内外数据库收录:
  • 美国数学评论（网络版）,德国数学文摘,中国中国科技核心期刊,中国北大核心期刊（2004版）,中国北大核心期刊（2008版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）,中国北大核心期刊（2000版）
  • 被引量:22973