Strongly irreducible operators on Banach spaces

被引：0
作者：
Yun Nan Zhang
Huai Jie Zhong
机构：
[1] Fujian Normal University,School of Mathematics and Computer Science
[2] Hebei Normal University,Mathematics and Information Science College
来源：
Acta Mathematica Sinica, English Series | 2012年 / 28卷
关键词：
Banach spaces; strongly irreducible operators; *-separable; quasisimilar; 46B20; 47A05;
D O I：
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学科分类号：
摘要：
This paper firstly discusses the existence of strongly irreducible operators on Banach spaces. It shows that there exist strongly irreducible operators on Banach spaces with w*-separable dual. It also gives some properties of strongly irreducible operators on Banach spaces. In particular, if T is a strongly irreducible operator on an infinite-dimensional Banach space, then T is not of finite rank and T is not an algebraic operator. On Banach spaces with subsymmetric bases, including infinite-dimensional separable Hilbert spaces, it shows that quasisimilarity does not preserve strong irreducibility. In addition, we show that the strong irreducibility of an operator does not imply the strong irreducibility of its conjugate operator, which is not the same as the property in Hilbert spaces.
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页码：727 / 740
页数：13
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