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

被引：3
|
作者：
Ma, Hai Feng [1 ]
Hudzik, Henryk [2 ]
Wang, Yu Wen [3 ]
Ma, Zhao Feng [4 ]
机构：
[1] Harbin Normal Univ, Sch Math Sci, Harbin 150025, Peoples R China
[2] Adam Mickiewicz Univ Poznan, Fac Math & Comp Sci, PL-61614 Poznan, Poland
[3] Harbin Normal Univ, Yuan Yung Tseng Funct Anal Res Ctr, Harbin 150025, Peoples R China
[4] Zhejiang Inst Commun, Dept Informat & Management, Hangzhou 311112, Zhejiang, Peoples R China
来源：
ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2010年 / 26卷 / 12期
基金：
中国国家自然科学基金;
关键词：
Locally fine point; rank theorem; narrow spectrum; spectral radius; invariant subspace; ADVANCED CALCULUS; RANK THEOREMS;
D O I：
10.1007/s10114-010-9329-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
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.
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页码：2349 / 2354
页数：6
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