Weyl's Theorem for Functions of Operators and Approximation

被引：41

作者：

Li, Chun Guang ^{[2
]}

Zhu, Sen ^{[1
]}

Feng, You Ling ^{[2
,3
]}

机构：

[1] Jilin Univ, Dept Math, Changchun 130012, Peoples R China

[2] Jilin Univ, Inst Math, Changchun 130012, Peoples R China

[3] Changchun Taxat Coll, Dept Appl Math, Changchun 130117, Peoples R China

来源：

INTEGRAL EQUATIONS AND OPERATOR THEORY | 2010年 / 67卷 / 04期

关键词：

Weyl's theorem; function of operators; small-compact closure; CLASS-A OPERATORS; HYPONORMAL-OPERATORS; RIESZ IDEMPOTENT; SPECTRUM;

D O I：

10.1007/s00020-010-1796-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let H be a complex separable infinite dimensional Hilbert space. In this paper, we characterize those operators T on H satisfying that Weyl's theorem holds for f(T) for each function f analytic on some neighborhood of sigma(T). Also, it is proved that, given an operator T on H and epsilon > 0, there exists a compact operator K with parallel to K parallel to < epsilon such that Weyl's theorem holds for T + K.

引用

页码：481 / 497

页数：17

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