| 摘要: |
| 本文研究Banach空间上有界算子4子空间系统ST,说明ST与ST'同构的充要条件是T与T'相似,也说明ST是不可分解的的充要条件是T是强不可约的,最后说明当Banach空间X的共轭空间X*w*可分时,X⊕X中存在不可数多个两两不同构的不可分解的有界算子4子空间系统.这些结果是Hilbert空间上相应结果到Banach空间上的推广与补充. |
| 关键词: Banach空间 有界算子系统 4子空间系统 强不可约算子 |
| DOI： |
| 分类号:O177.2 |
| 基金项目:国家自然科学基金资助 (11971108). |
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| BOUNDED OPERATOR FOUR SUBSPACE SYSTEMS IN BANACH SPACES |
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CHEN Jian-lan, QUE Jia-hua, ZHANG Yun-nan
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School of Mathematics and Statistics, Fujian Normal University, Fuzhou 350117, China
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| Abstract: |
| This paper studies the bounded operator four subspaces systems ST in Banach spaces. It shows that ST and ST' are isomorphic if and only if T and T' are similar. It also shows that ST is indecomposable if and only if T is strongly irreducible. Finally, it shows that when the conjugate space X* of Banach space X is w* separable, there is an uncountable family of indecomposable bounded operator four subspace systems in X⊕X which are not isomorphic each other. These results are the generalizations and supplements of the corresponding results on Hilbert spaces to Banach spaces. |
| Key words: Banach spaces bounded operator systems four subspace systems strongly irreducible operators |
