2 × 2上三角型算子矩阵的拟Fredholm谱
The Quasi-Fredholm Spectrum of 2 × 2 Upper Triangular Operator Matrices
DOI: 10.12677/pm.2025.154118, PDF,    国家自然科学基金支持
作者: 包中秀, 吴德玉*：内蒙古大学数学科学学院，内蒙古 呼和浩特
关键词: 半正则算子；拟Fredholm算子；算子矩阵；Semi-Regular Operator； Quasi-Fredholm Operator； Operator Matrices
摘要: 主要运用内部项的拟Fredholm性质研究了2 × 2上三角型算子矩阵的拟Fredholm谱，并拓展到无界2 × 2上三角型算子矩阵的拟Fredholm谱。给出了具体例子加以说明结论的有效性。
Abstract: The Quasi-Fredholm Spectrum of 2 × 2 upper triangular operator matrices is studied by using the Quasi-Fredholm property of its internal entries, and extended to the Quasi-Fredholm spectrum of the triangular operator matrices on the unbounded 2 × 2. The example is given to illustrate the validity of the result.
文章引用：包中秀, 吴德玉. 2 × 2上三角型算子矩阵的拟Fredholm谱[J]. 理论数学, 2025, 15(4): 151-161. https://doi.org/10.12677/pm.2025.154118

参考文献

[1] Kato, T. (1958) Perturbation Theory for Nullity, Deficiency and Other Quantities of Linear Operators. Journal d’Analyse Mathématique, 6, 261-322. [Google Scholar] [CrossRef] 
[2] Labrousse, J. (1980) Les operateurs quasi Fredholm: Une generalisation des operateurs semi Fredholm. Rendiconti del Circolo Matematico di Palermo, 29, 161-258. [Google Scholar] [CrossRef] 
[3] Mbekhta, M. (1996) On the Axiomatic Theory of Spectrum II. Studia Mathematica, 119, 129-147. [Google Scholar] [CrossRef] 
[4] Apostol, C. (1985) The Reduced Minimum Modulus. Michigan Mathematical Journal, 32, 279-294. [Google Scholar] [CrossRef] 
[5] Mbekhta, M. and Ouahab, A. (1994) Opérateur srégulier dans un espace de Banach et théorie spectrale. Acta Scientiarum Mathematicarum, 59, 525-544.
[6] Barraa, M. and Boumazgour, M. (2003) On the Perturbations of Spectra of Upper Triangular Operator Matrices. Abdus Salam International Centre for Theoretical Physics, 17.
[7] García, O., Causil, D., Sanabria, J. and Carpintero, C. (2018) New Decompositions for the Classes of Quasi-Fredholm and Semi b-Weyl Operators. Linear and Multilinear Algebra, 68, 750-763. [Google Scholar] [CrossRef] 
[8] Gupta, A. and Kumar, A. (2020) Quasi-Fredholm Spectrum and Compact Perturbations. Complex Analysis and Operator Theory, 14, 1-9. [Google Scholar] [CrossRef] 
[9] Aiena, P. (2004) Fredholm and Local Spectral Theory, with Applications to Multipliers. Kluwer Academic Publishers, 1-452.
[10] Benharrat, M. and Messirdi, B. (2014) Relationship between the Essential Quasi-Fredholm Spectrum and the Closed-range Spectrum. Analele Universitătii Oradea Fasc. Matematica, 21, 5-12.
[11] Benharrat, M., Ammar, A., Jeribi, A., et al. (2014) On the Kato, Semi-Regular and Essentially Semi-Regular Spectra. Functional Analysis, Approximation and Computation, 6, 9-22.
[12] El, O., Ech-Cherif, E. and Karmouni, M. (2022) Quasi-Fredholm Spectrum for Operator Matrices. Filomat, 36, 4893-4902. [Google Scholar] [CrossRef] 
[13] Aiena, P. (2018) Fredholm and Local Spectral Theory II, With Application to Weyl-Type Theorems. Springer, 1-552.
[14] Benharrat, M. and Messirdi, B. (2011) On the Generalized Kato Spectrum. Serdica Mathematical Journal, 37, 283-294.
[15] 阿拉坦仓, 吴德玉, 黄俊杰, 侯国林. 无穷维Hamilton算子谱分析[M]. 北京: 高等教育出版社, 2023: 1-349.
[16] 吴德玉, 阿拉坦仓. 分块算子矩阵谱理论及其应用[M]. 北京: 科学出版社, 2013: 1-230.

为你推荐