Banach空间中的有界算子4子空间系统  

BOUNDED OPERATOR FOUR SUBSPACE SYSTEMS IN BANACH SPACES

作　　者：陈剑岚 阙佳华 张云南[1] CHEN Jian-lan;QUE Jia-hua;ZHANG Yun-nan(School of Mathematics and Statistics,Fujian Normal University,Fuzhou 350117,China)

机构地区：[1]福建师范大学数学与统计学院,福建福州350117

出　　处：《数学杂志》2024年第2期182-188,共7页Journal of Mathematics

基　　金：国家自然科学基金资助(11971108).

摘　　要：本文研究Banach空间上有界算子4子空间系统S_(T),说明S_(T)与S_(T0)同构的充要条件是T与T_(0)相似,也说明S_(T)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.This paper studies the bounded operator four subspaces systems S_(T)in Banach spaces.It shows that S_(T)and S_(T0)are isomorphic if and only if T and T_(0)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 L X which are not isomorphic each other.These results are the generalizations and supplements of the corresponding results on Hilbert spaces to Banach spaces.

关 键 词：BANACH空间 有界算子系统 4子空间系统 强不可约算子 

分 类 号：O177.2[理学—数学]