The spectral properties of [m] $[m]$-complex symmetric operators
Abstract In this paper, we introduce the class of [m]-complex symmetric operators and study various properties of this class. In particular, we show that if T is an [m]-complex symmetric operator, then Tn $T^{n}$ is also an [m]-complex symmetric operator for any n∈N $n\in\mathbb {N}$. In addition, w...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-08-01
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| Series: | Journal of Inequalities and Applications |
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| Online Access: | http://link.springer.com/article/10.1186/s13660-018-1800-1 |
| _version_ | 1819290235261943808 |
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| author | Junli Shen |
| author_facet | Junli Shen |
| author_sort | Junli Shen |
| collection | DOAJ |
| description | Abstract In this paper, we introduce the class of [m]-complex symmetric operators and study various properties of this class. In particular, we show that if T is an [m]-complex symmetric operator, then Tn $T^{n}$ is also an [m]-complex symmetric operator for any n∈N $n\in\mathbb {N}$. In addition, we prove that if T is an [m]-complex symmetric operator, then σa(T) $\sigma_{a}(T)$, σSVEP(T) $\sigma_{\mathrm{SVEP}}(T)$, σβ(T) $\sigma_{\beta }(T)$, and σ(β)ϵ(T) $\sigma_{(\beta)_{\epsilon}}(T)$ are symmetric about the real axis. Finally, we investigate the stability of an [m]-complex symmetric operator under perturbation by nilpotent operators commuting with T. |
| first_indexed | 2024-12-24T03:19:31Z |
| format | Article |
| id | doaj.art-63da5cef80af47a2b13a30dffb69d706 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-24T03:19:31Z |
| publishDate | 2018-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-63da5cef80af47a2b13a30dffb69d7062022-12-21T17:17:32ZengSpringerOpenJournal of Inequalities and Applications1029-242X2018-08-01201811910.1186/s13660-018-1800-1The spectral properties of [m] $[m]$-complex symmetric operatorsJunli Shen0College of Computer and Information Technology, Henan Normal UniversityAbstract In this paper, we introduce the class of [m]-complex symmetric operators and study various properties of this class. In particular, we show that if T is an [m]-complex symmetric operator, then Tn $T^{n}$ is also an [m]-complex symmetric operator for any n∈N $n\in\mathbb {N}$. In addition, we prove that if T is an [m]-complex symmetric operator, then σa(T) $\sigma_{a}(T)$, σSVEP(T) $\sigma_{\mathrm{SVEP}}(T)$, σβ(T) $\sigma_{\beta }(T)$, and σ(β)ϵ(T) $\sigma_{(\beta)_{\epsilon}}(T)$ are symmetric about the real axis. Finally, we investigate the stability of an [m]-complex symmetric operator under perturbation by nilpotent operators commuting with T.http://link.springer.com/article/10.1186/s13660-018-1800-1[ m ] $[m]$ -complex symmetric operatorProperty (β)Nilpotent operator |
| spellingShingle | Junli Shen The spectral properties of [m] $[m]$-complex symmetric operators Journal of Inequalities and Applications [ m ] $[m]$ -complex symmetric operator Property (β) Nilpotent operator |
| title | The spectral properties of [m] $[m]$-complex symmetric operators |
| title_full | The spectral properties of [m] $[m]$-complex symmetric operators |
| title_fullStr | The spectral properties of [m] $[m]$-complex symmetric operators |
| title_full_unstemmed | The spectral properties of [m] $[m]$-complex symmetric operators |
| title_short | The spectral properties of [m] $[m]$-complex symmetric operators |
| title_sort | spectral properties of m m complex symmetric operators |
| topic | [ m ] $[m]$ -complex symmetric operator Property (β) Nilpotent operator |
| url | http://link.springer.com/article/10.1186/s13660-018-1800-1 |
| work_keys_str_mv | AT junlishen thespectralpropertiesofmmcomplexsymmetricoperators AT junlishen spectralpropertiesofmmcomplexsymmetricoperators |