Property  (ω)  for Bounded Linear Operators and Its Stability

doi:10.3969/j.issn.1006-8074.2025.02.003

Mathematical Theory and Applications ›› 2025, Vol. 45 ›› Issue (2): 40-52.doi: 10.3969/j.issn.1006-8074.2025.02.003

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Property (ω) for Bounded Linear Operators and Its Stability

DAI Lei$^1,*, YI Jialu², CAO Xiaohong²

1. School of Mathematics and Statistics, Weinan Normal University, Weinan 714099, China; 2. School of Mathematics and Statistics, Shanxi Normal University, Xian 710119, China

Online:2025-06-28 Published:2025-08-09
Supported by:
This work is supported by the National Natural Science Foundation of China (No. 11501419) and the Nature Science Basic Research Plan in Shaanxi Province of China (No. 2021JM-519)

Abstract

Abstract: In this paper, using the property of uniform Fredholm non-positive index of bounded linear operators, we give criteria for operators and their functions to possess property $(\omega)$, and several equivalent conditions for the stability of property $(\omega)$, and investigate the relationship between the stability of property $(\omega)$ and the $(\omega)$-property of operator functions.

Key words: Functional calculus, Property $(\omega)$, Spectrum, Stability, $CFI_-$ operator

DAI Lei, YI Jialu, CAO Xiaohong. Property (ω) for Bounded Linear Operators and Its Stability[J]. Mathematical Theory and Applications, 2025, 45(2): 40-52.

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Property (ω) for Bounded Linear Operators and Its Stability

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