| Banach空间结构和算子构成的互动作用 |
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| 引用本文： | 钟怀杰,江樵芬. Banach空间结构和算子构成的互动作用[J]. 数学进展, 2007, 36(5): 530-538 |
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| 作者姓名： | 钟怀杰 江樵芬 |
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| 作者单位： | 福建师范大学数学系,福州,福建,350007 |
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| 基金项目： | 国家自然科学基金;福建省自然科学基金 |
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| 摘 要： | 从Banach空间结构和算子构成的互动作用这一视角,介绍Gowers-Maurey系列成果研究深化的某些新动向.全文分为:H.I.型空间研究新成果;G-M基本定理与"平方-立方猜想";本性不可比空间与G猜想;Pisier空间相关研究和关于K群K_i(B(X))的一些猜想等5小节.
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| 关 键 词： | Banach 空间结构 动作 算子 G猜想 空间相关 立方 平方 |
| 文章编号： | 1000-0917（2007）05-0530-09 |
| 修稿时间： | 2005-09-09 |
The Interaction Between the Structure of Banach Spaces and Operators |
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| ZHONG Huaijie,JIANG Qiaofen. The Interaction Between the Structure of Banach Spaces and Operators[J]. Advances in Mathematics(China), 2007, 36(5): 530-538 |
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| Authors: | ZHONG Huaijie JIANG Qiaofen |
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| Affiliation: | The Mathematical Department of Fujian Normal University, Fuzhou, Fujian, 350007, P. R. China |
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| Abstract: | In the viewpoint of the interaction between the structure of Banach spaces and operators,this paper introduces some recent developments about a series of the Gowers and Maurey's results.It composes of five sections.They include some results about the study of H. I.spaces;G-M's Basic Theorem and the"square-Cubic Conjecture";Essentionally incomparable Banach spaces and the conjecture of M.Gonzalez;Related studies to Pisier's Space;And some conjectures of the K-groups K_i(B(X)) of some Banach space X. |
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| Keywords: | Banach space H.I.space operator Banach algebra K_0-group |
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