The Judgment of Weyl's Theorem and Property (<i>R</i>)

ZHAO Jutao; CAO Xiaohong; DONG Jiong

doi:10.6054/j.jscnun.2023026

Journal of South China Normal University (Natural Science Edition) > 2023 > 55(2): 109-115. > DOI: 10.6054/j.jscnun.2023026

ZHAO Jutao, CAO Xiaohong, DONG Jiong. The Judgment of Weyl's Theorem and Property (R)[J]. Journal of South China Normal University (Natural Science Edition), 2023, 55(2): 109-115. DOI: 10.6054/j.jscnun.2023026

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The Judgment of Weyl's Theorem and Property (R)

1.
Department of Mathematics, Changzhi University, Changzhi 046011, China
2.
School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710119, China

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Received Date: October 23, 2021
Available Online: June 13, 2023

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Abstract

Abstract

The perturbation invariance of semi-Fredholm operators are used to study Weyl type theorems for boun-ded linear operators and upper triangular operator matrices. First, the necessary and sufficient conditions for which both the property(R₁) and Browder's theorem hold or both the property (R) and Weyl's theorem hold for bounded linear operators are given. In addition, the conditions for which both the property (R) and Weyl's theorem hold for upper triangular operator matrices are explored.
- bounded linear operator,
- upper triangular operator matrix,
- property (R),
- Weyl's theorem,
- spectrum

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