On the $A$-$q$-Numerical Range of Operators in Semi-Hilbertian Spaces
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914143042273280 |
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| author | Rani, Jyoti Patra, Arnab Birbonshi, Riddhick |
| author_facet | Rani, Jyoti Patra, Arnab Birbonshi, Riddhick |
| contents | This study investigates the $A$-$q$-numerical range of an operator within the framework of semi-Hilbertian spaces. Several fundamental properties of the $A$-$q$-numerical range are established, including spectral inclusion results and a disk union formula. Bounds for the $A$-$q$-numerical radius are derived, extending and generalizing previously known results. Finally, the notion of $A$-nilpotent operator is introduced, and it is shown that the $A$-$q$-numerical range of an $A$-nilpotent operator with index $2$ is a disk (open or closed) in the complex plane. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_19855 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the $A$-$q$-Numerical Range of Operators in Semi-Hilbertian Spaces Rani, Jyoti Patra, Arnab Birbonshi, Riddhick Functional Analysis 46C05 (Primary) 15A60, 47A05, 47A12 (Secondary) This study investigates the $A$-$q$-numerical range of an operator within the framework of semi-Hilbertian spaces. Several fundamental properties of the $A$-$q$-numerical range are established, including spectral inclusion results and a disk union formula. Bounds for the $A$-$q$-numerical radius are derived, extending and generalizing previously known results. Finally, the notion of $A$-nilpotent operator is introduced, and it is shown that the $A$-$q$-numerical range of an $A$-nilpotent operator with index $2$ is a disk (open or closed) in the complex plane. |
| title | On the $A$-$q$-Numerical Range of Operators in Semi-Hilbertian Spaces |
| topic | Functional Analysis 46C05 (Primary) 15A60, 47A05, 47A12 (Secondary) |
| url | https://arxiv.org/abs/2502.19855 |