a-Weyl's Theorem and Property(\mathcalR ) for Operator Functions

ZHAO Lingling; GAO Kai; HONG Mingli; WANG Fuchang

doi:10.6054/j.jscnun.2023066

Journal of South China Normal University (Natural Science Edition) > 2023 > 55(5): 80-87. > DOI: 10.6054/j.jscnun.2023066

ZHAO Lingling, GAO Kai, HONG Mingli, WANG Fuchang. a-Weyl's Theorem and Property(

$\mathcal{R}$ ) for Operator Functions[J]. Journal of South China Normal University (Natural Science Edition), 2023, 55(5): 80-87. DOI: 10.6054/j.jscnun.2023066

Citation:

ZHAO Lingling, GAO Kai, HONG Mingli, WANG Fuchang. a-Weyl's Theorem and Property(

$\mathcal{R}$ ) for Operator Functions[J]. Journal of South China Normal University (Natural Science Edition), 2023, 55(5): 80-87. DOI: 10.6054/j.jscnun.2023066

ZHAO Lingling, GAO Kai, HONG Mingli, WANG Fuchang. a-Weyl's Theorem and Property(

$\mathcal{R}$ ) for Operator Functions[J]. Journal of South China Normal University (Natural Science Edition), 2023, 55(5): 80-87. DOI: 10.6054/j.jscnun.2023066

Citation:

ZHAO Lingling, GAO Kai, HONG Mingli, WANG Fuchang. a-Weyl's Theorem and Property(

$\mathcal{R}$ ) for Operator Functions[J]. Journal of South China Normal University (Natural Science Edition), 2023, 55(5): 80-87. DOI: 10.6054/j.jscnun.2023066

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a-Weyl's Theorem and Property( $\mathcal{R}$ ) for Operator Functions

1.
Basic Courses Department, Institute of Disaster Prevention, Sanhe 065201, China
2.
School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710119, China

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Received Date: April 04, 2022
Available Online: January 21, 2024

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Abstract

Abstract

The new judgements for which a-Weyl's theorem, property ( $\mathcal{R}$ ), both a-Weyl's theorem and property ( $\mathcal{R}$ ) hold are given. In additional, the necessary and sufficient conditions for operator functions to satisfy the a-Weyl's theorem, the property ( $\mathcal{R}$ ), both the a-Weyl's theorem and the property ( $\mathcal{R}$ ) are considered.
- a-Weyl's theorem,
- property( $\mathcal{R}$ ),
- operator function,
- spectrum

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a-Weyl's Theorem and Property(R\mathcal{R} ) for Operator Functions

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a-Weyl's Theorem and Property( $\mathcal{R}$ ) for Operator Functions