Weyl's theorem for bounded linear operators and its functional calculus

doi:10.13471/j.cnki.acta.snus.2020.02.003

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Weyl's theorem for bounded linear operators and its functional calculus

更新时间：2023-12-11

- Weyl's theorem for bounded linear operators and its functional calculus
- Acta Scientiarum Naturalium Universitatis SunYatseni Vol. 59, Issue 2, Pages: 22-27(2020)
- 作者机构：
  
  1. 长治学院数学系,山西,长治,046011
  2. 陕西师范大学数学与信息科学学院,陕西,西安,710119
- 作者简介：
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.2020.02.003
  CLC：
- Published：2020，
  
  Published Online：25 March 2020，
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Weyl's theorem for bounded linear operators and its functional calculus. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 59(2):22-27(2020)
DOI：

Weyl's theorem for bounded linear operators and its functional calculus. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 59(2):22-27(2020) DOI： 10.13471/j.cnki.acta.snus.2020.02.003.

摘要

令

B(H)

为无限复可分的 Hilbert 空间

上的有界线性算子全体。若

T∈B(H)

定义

H(T)

为在

的谱集

σ(T)

的某个邻域上解析但在

σ(T)

的任一分支上不为常数的函数全体。利用新定义的谱集，研究了算子

及

f(T)(f∈H(T))

的 Weyl 定理，并刻画了

和

(T)

满足 Weyl 定理的等价条件。另外利用所得的结论，探索了

hyponormal(或

-hyponormal)算子的 Weyl 定理。

Abstract

Let

B(H)

be the set of all bounded linear operators on an infinite dimensional separable complex Hilbert space H. If

T∈B(H)

the set of all functions

which are analytic on a neighbourhood of σ(T) and are not constants on any component of

σ(T)

is denoted by H(T). Using the new spectrum

Weyls theorem for

T∈B(H)

and

f(T) (f∈H(T))

is studied

and the necessary and sufficient conditions for both T and

f(T)

satisfying Weyl's theorem are characterized. Moreover

Weyls theorem for

hyponormal (or

M-

hyponormal) operators are explored.

关键词

Browder 定理Weyl 定理谱p-hyponormal&nbsp算子

Keywords

Browders theoremWeyls theoremspectrump-hyponormaloperators

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