The generalized regular points and narrow spectrum points of bounded linear operators on Hilbert spaces

被引：0

作者：

Hai Feng Ma

Henryk Hudzik

Yu Wen Wang

Zhao Feng Ma

机构：

[1] Harbin Normal University,School of Mathematical Science

[2] Adam Mickiewicz University,Faculty of Mathematics and Computer Science

[3] Harbin Normal University,Yuan

[4] Zhejiang Institute of Communications,Yung Tseng Functional Analysis Research Center

来源：

Acta Mathematica Sinica, English Series | 2010年 / 26卷

关键词：

Locally fine point; rank theorem; narrow spectrum; spectral radius; invariant subspace; 47A05; 47A10; 47A11;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

In this paper, we introduce the concepts of generalized regular points and narrow spectrum points of bounded linear operators on Hilbert spaces. The concept of generalized regular points is an extension of the concept regular points, and so, the set of all spectrum points is reduced to the narrow spectrum. We present not only the same and different properties of spectrum and of narrow spectrum but also show the relationship between them. Finally, the well known problem about the invariant subspaces of bounded linear operators on separable Hilbert spaces is simplified to the problem of the operator with narrow spectrum only.

引用

页码：2349 / 2354

页数：5

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