| Some Characterizations of Hereditarily Indecomposable Banach Spaces |
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| 作者姓名： | 苏维钢 钟怀杰 |
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| 作者单位： | School of Mathematics and Computer Science Fujian Normal University Fuzhou，350007，School of Mathematics and Computer Science，Fujian Normal University，Fuzhou，350007 |
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| 基金项目： | The NNSF (10471025) of China
the Foundation (JA04170) of the Education Department of Fujian Province, China. |
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| 摘 要： | In this paper we first discuss the relations between some G-M-type spaces, and the previous eight kinds of G-M-type Banach spaces are merged into four different kinds. Then we build a Generalized Operator Extension Theorem, and introduce the concept of complete minimal sequences. Some sufficient and necessary conditions under which a Banach space is a hereditarily indecomposable space are given. Finally, we give some characterizations of hereditarily indecomposable Banach Spaces.
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| 关 键 词： | Banach空间 遗传不可分解系统 最小序列 扩展理论 |
Some Characterizations of Hereditarily Indecomposable Banach Spaces |
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| SU Wei-gangand ZHONG Huai-jie.Some Characterizations of Hereditarily Indecomposable Banach Spaces[J].Northeastern Mathematical Journal,2005,21(4):439-446. |
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| Authors: | SU Wei-gangand ZHONG Huai-jie |
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| Institution: | School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, 350007 |
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| Abstract: | In this paper we first discuss the relations between some G-M-type spaces, and the previous eight kinds of G-M-type Banach spaces are merged into four different kinds. Then we build a Generalized Operator Extension Theorem, and introduce the concept of complete minimal sequences. Some sufficient and necessary conditions under which a Banach space is a hereditarily indecomposable space are given. Finally, we give some characterizations of hereditarily indecomposable Banach Spaces. |
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| Keywords: | Banach space hereditarily indecomposable complete minimal sequence M-basis |
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