首页 | 本学科首页   官方微博 | 高级检索  
     检索      

Banach空间结构理论的重大进展--关于Gowers-Maurey系列成果
引用本文:钟怀杰.Banach空间结构理论的重大进展--关于Gowers-Maurey系列成果[J].数学进展,2000,29(1):1-18.
作者姓名:钟怀杰
作者单位:福建师范大学数学系,福州,福建,350007,中国
基金项目:中国科学院资助项目,福建省自然科学基金 
摘    要:最近,GowersW.T.和MaureyB.构造出第一例遗传不可分解空间,否定地解决了无条件基序列问题,由此导致了Banach空间的结构理论研究中系列问题的解决,本综述介绍这一新动向,反映了G-M系列成果,全文分为七个部分,1个历史回顾与问题沿革;2.G-M空间XG1及其遗传不可分解性质,3.关于空间XG1上的算子构成;4个关于共轭空间XG1,5.关于G-M的系列成果,6.G-M型空间构造的

关 键 词:G-M型空间  无条件基序列  巴拿赫空间  算子

The Significant Development in the Structural Theory of Banach Spaces--On a Series of theGowers-Maurey's Results
Zhong Huaijie.The Significant Development in the Structural Theory of Banach Spaces--On a Series of theGowers-Maurey''s Results[J].Advances in Mathematics,2000,29(1):1-18.
Authors:Zhong Huaijie
Abstract:Recently Gowers W.T. and Maurey B. constructed the first example XG1 of the hereditarily indecomposable Banach spaces containing no unconditional basic sequence. Some further studies and reconstructions of this space result in some satisfactory answers of a series of open questions in the Banach spaces theory. In this paper, recent developments about this direction have been introduced. It composes of the following seven sections: 1. A review of the history and the evolution of the problems, 2. The G-M space and its hereditarily indecomposable property; 3. On the operators on the space XG1;4. On the conjugate space XG1;5. On a series of G-M's results; 6. A new viewpotint of construction of G-M-type space; 7. A list of open problems.
Keywords:Banach space  unconditional  basic sequence  hereditarily indecomposable space  quotient incompound able space  strictly singular operator  strictly cosingular operator
本文献已被 CNKI 维普 万方数据 等数据库收录!
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号