Weyl-Type Theorems of Upper Triangular Relation Matrices
The spectral theory of operator matrices has several applications in elasticity, quantum mechanics, fluid dynamics, and other fields of mathematical physics. The study of operator matrices is more challenging when the involved operators are not single-valued and should be studied in the context of t...
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MDPI AG
2024-11-01
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| author | Yanyan Du Junjie Huang |
| author_facet | Yanyan Du Junjie Huang |
| author_sort | Yanyan Du |
| collection | DOAJ |
| description | The spectral theory of operator matrices has several applications in elasticity, quantum mechanics, fluid dynamics, and other fields of mathematical physics. The study of operator matrices is more challenging when the involved operators are not single-valued and should be studied in the context of the theory of relations. In this paper, we utilize the connection between linear relations and their induced operators and use space decomposition methods to characterize the distribution of the spectrum for upper triangular relation matrices. We undertake the same for the essential spectrum, Weyl spectrum, and Browder spectrum. Under certain conditions, we obtain a Browder-type theorem and a Weyl-type theorem for such relation matrices. |
| format | Article |
| id | doaj-art-2bbba7d1853941ebb0e7523b42b2a4c5 |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-11-01 |
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| series | Mathematics |
| spelling | doaj-art-2bbba7d1853941ebb0e7523b42b2a4c52025-08-20T02:50:33ZengMDPI AGMathematics2227-73902024-11-011223375210.3390/math12233752Weyl-Type Theorems of Upper Triangular Relation MatricesYanyan Du0Junjie Huang1School of Mathematics and Statistics, Shandong University of Technology, Zibo 255000, ChinaSchool of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, ChinaThe spectral theory of operator matrices has several applications in elasticity, quantum mechanics, fluid dynamics, and other fields of mathematical physics. The study of operator matrices is more challenging when the involved operators are not single-valued and should be studied in the context of the theory of relations. In this paper, we utilize the connection between linear relations and their induced operators and use space decomposition methods to characterize the distribution of the spectrum for upper triangular relation matrices. We undertake the same for the essential spectrum, Weyl spectrum, and Browder spectrum. Under certain conditions, we obtain a Browder-type theorem and a Weyl-type theorem for such relation matrices.https://www.mdpi.com/2227-7390/12/23/3752relation matrixessential spectrumWeyl spectrumBrowder-type theoremWeyl-type theorem |
| spellingShingle | Yanyan Du Junjie Huang Weyl-Type Theorems of Upper Triangular Relation Matrices Mathematics relation matrix essential spectrum Weyl spectrum Browder-type theorem Weyl-type theorem |
| title | Weyl-Type Theorems of Upper Triangular Relation Matrices |
| title_full | Weyl-Type Theorems of Upper Triangular Relation Matrices |
| title_fullStr | Weyl-Type Theorems of Upper Triangular Relation Matrices |
| title_full_unstemmed | Weyl-Type Theorems of Upper Triangular Relation Matrices |
| title_short | Weyl-Type Theorems of Upper Triangular Relation Matrices |
| title_sort | weyl type theorems of upper triangular relation matrices |
| topic | relation matrix essential spectrum Weyl spectrum Browder-type theorem Weyl-type theorem |
| url | https://www.mdpi.com/2227-7390/12/23/3752 |
| work_keys_str_mv | AT yanyandu weyltypetheoremsofuppertriangularrelationmatrices AT junjiehuang weyltypetheoremsofuppertriangularrelationmatrices |