Browder spectra of closed upper triangular operator matrices
Let $ T_{B} = \left[\begin{array}{ll} A & B \\ 0 & D \end{array}\right] $ be an unbounded upper operator matrix with diagonal domain, acting in $ \mathcal H \oplus\mathcal K $, where $ \mathcal H $ and $ \mathcal K $ are Hilbert spaces. In this paper, some sufficient and necessary co...
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AIMS Press
2024-01-01
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2024248?viewType=HTML |
| _version_ | 1797322554487078912 |
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| author | Qingmei Bai Alatancang Chen Jingying Gao |
| author_facet | Qingmei Bai Alatancang Chen Jingying Gao |
| author_sort | Qingmei Bai |
| collection | DOAJ |
| description | Let $ T_{B} = \left[\begin{array}{ll} A & B \\ 0 & D \end{array}\right] $ be an unbounded upper operator matrix with diagonal domain, acting in $ \mathcal H \oplus\mathcal K $, where $ \mathcal H $ and $ \mathcal K $ are Hilbert spaces. In this paper, some sufficient and necessary conditions are characterized under which $ T_{B} $ is Browder (resp., invertible) for some closable operator $ B $ with $ \mathcal D(B)\supset \mathcal D(D) $. Further, a sufficient and necessary condition is given under which the Browder spectrum (resp., spectrum) of $ T_{B} $ coincides with the union of the Browder spectrum (resp., spectrum) of its diagonal entries. |
| first_indexed | 2024-03-08T05:14:59Z |
| format | Article |
| id | doaj.art-507fa716f46d491c8ce9a6f52a155d4e |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-08T05:14:59Z |
| publishDate | 2024-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-507fa716f46d491c8ce9a6f52a155d4e2024-02-07T01:31:08ZengAIMS PressAIMS Mathematics2473-69882024-01-01925110512110.3934/math.2024248Browder spectra of closed upper triangular operator matricesQingmei Bai0Alatancang Chen1Jingying Gao21. School of Mathematical Sciences, Hohhot Minzu College, Hohhot, 010051, China 2. Key Laboratory of Infinite-dimensional Hamiltonian System and Its Algorithm Application (Inner Mongolia Normal University), Ministry of Education, Hohhot, 010022, China 3. Center for Applied Mathematics Inner Mongolia, Hohhot, 010022, China1. School of Mathematical Sciences, Hohhot Minzu College, Hohhot, 010051, China 2. Key Laboratory of Infinite-dimensional Hamiltonian System and Its Algorithm Application (Inner Mongolia Normal University), Ministry of Education, Hohhot, 010022, China 3. Center for Applied Mathematics Inner Mongolia, Hohhot, 010022, China1. School of Mathematical Sciences, Hohhot Minzu College, Hohhot, 010051, ChinaLet $ T_{B} = \left[\begin{array}{ll} A & B \\ 0 & D \end{array}\right] $ be an unbounded upper operator matrix with diagonal domain, acting in $ \mathcal H \oplus\mathcal K $, where $ \mathcal H $ and $ \mathcal K $ are Hilbert spaces. In this paper, some sufficient and necessary conditions are characterized under which $ T_{B} $ is Browder (resp., invertible) for some closable operator $ B $ with $ \mathcal D(B)\supset \mathcal D(D) $. Further, a sufficient and necessary condition is given under which the Browder spectrum (resp., spectrum) of $ T_{B} $ coincides with the union of the Browder spectrum (resp., spectrum) of its diagonal entries.https://www.aimspress.com/article/doi/10.3934/math.2024248?viewType=HTMLclosed operatoroperator matrixbrowder spectrumspectrum |
| spellingShingle | Qingmei Bai Alatancang Chen Jingying Gao Browder spectra of closed upper triangular operator matrices AIMS Mathematics closed operator operator matrix browder spectrum spectrum |
| title | Browder spectra of closed upper triangular operator matrices |
| title_full | Browder spectra of closed upper triangular operator matrices |
| title_fullStr | Browder spectra of closed upper triangular operator matrices |
| title_full_unstemmed | Browder spectra of closed upper triangular operator matrices |
| title_short | Browder spectra of closed upper triangular operator matrices |
| title_sort | browder spectra of closed upper triangular operator matrices |
| topic | closed operator operator matrix browder spectrum spectrum |
| url | https://www.aimspress.com/article/doi/10.3934/math.2024248?viewType=HTML |
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