广义(ω)性质
The Generalized Property (ω)
摘要: Weyl定理作为算子谱理论的重要研究内容，被广泛应用在代数几何，线性空间理论，拓扑学等不同的数学分支中，有很大的应用和理论价值。本文基于已有的理论知识，研究Weyl定理的变化，结合广义Kato型算子定义的谱集ρgk(T)，给出Hilbert空间上有界线性算子满足广义(ω)性质的判定条件。
Abstract: As an important research content of operator spectrum theory, Weyl theorem is widely used in al-gebraic geometry, linear space theory, topology and other different branches of mathematics, and has great application and theoretical value. In this paper, based on the existing theoretical knowledge, we study the variation of Weyl theorem, combine with the spectrum set ρgk(T) defined by the generalized Kato type operators, and give the judgment conditions for the bounded opera-tors on Hilbert space to satisfy the generalized properties (ω).
文章引用：郑宇洁, 刘爱芳. 广义(ω)性质[J]. 应用数学进展, 2023, 12(5): 2152-2158. https://doi.org/10.12677/AAM.2023.125219

参考文献

[1] Gong, W.B. and Han, D.G. (1994) Spectrum of the Products of Operators and Compact Perturbations. Proceedings of the American Mathematical Society, 120, 755-760. [Google Scholar] [CrossRef] 
[2] Weyl, H. (1909) Über beschränkte quadratische Formen, deren Differenz vollstetig ist. Rendiconti del Circolo Matematico di Palermo (1884-1940), 27, 373-392. [Google Scholar] [CrossRef] 
[3] Harte, R. and Lee, W.Y. (1997) Another Note on Weyl’s Theorem. Transactions of the American Mathematical Society, 349. [Google Scholar] [CrossRef] 
[4] Rakoevi, V. (1989) Operators Obeying α-Weyl’s Theorem. Revue Roumaine de Mathématique Pures et Appliquées, 34, 915-919.
[5] Rakoevi, V. (1985) On a Class of Operators. Matematički Vesnik, 37, 423-426.
[6] Aiena, P. and Pea, P. (2006) Variations on Weyl’s Theorem. Journal of Mathe-matical Analysis and Applications, 324, 566-579. [Google Scholar] [CrossRef] 
[7] Aiena, P. (2004) Fredholm and Local Spectral Theory, with Applications to Multipliers. Springer Netherlands.
[8] Aiena, P. and Biondi, M.T. (2007) Property(ω) and Perturbations. Journal of Mathematical Analysis and Applications, 336, 683-692. [Google Scholar] [CrossRef] 
[9] Harte, R.E. (1996) On Kato Non-Singularity. Studia Mathematica, 117, 107-114. [Google Scholar] [CrossRef] 
[10] Djordjevic, D.S. (2002) Operators Consistent in Regularity. Publi-cationes Mathematicae Debrecen, 60, 1-15. [Google Scholar] [CrossRef] 
[11] Cao, X., Zhang, H. and Zhang, Y. (2010) Consistent Invertibility and Weyl’s Theorem. Journal of Mathematical Analysis and Applications, 369, 258-264. [Google Scholar] [CrossRef] 
[12] Dai, L., Cao, X.H. and Sun, C.H. (2010) A Note on Generalized Property(ω). Acta Mathematica Sinica, Chinese Series, 53, 219-226.
[13] Kato, T. (1966) Perturbation Theory for Line-ar Operators. Springer-Verlag New York Inc. [Google Scholar] [CrossRef] 

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