Spectrum and Fine Spectrum of Band Matrices Generated by Oscillatory Sequences
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866912192694059008 |
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| author | Rani, Jyoti Patra, Arnab Srivastava, P D |
| author_facet | Rani, Jyoti Patra, Arnab Srivastava, P D |
| contents | In this paper, a new class of band matrices is considered where the entries of each non-zero band form a sequence with two limit points. The compact perturbation technique is used to study the spectrum over the $\ell_{p}, (1<p<\infty)$ sequence space. Several spectral subdivisions such as fine spectrum, discrete spectrum, essential spectrum, etc. are obtained. In addition, a few sufficient conditions on the absence of point spectrum over the essential spectrum are also discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_09302 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Spectrum and Fine Spectrum of Band Matrices Generated by Oscillatory Sequences Rani, Jyoti Patra, Arnab Srivastava, P D Spectral Theory Functional Analysis Primary 47A10 (Primary), 47B37 (Secondary) In this paper, a new class of band matrices is considered where the entries of each non-zero band form a sequence with two limit points. The compact perturbation technique is used to study the spectrum over the $\ell_{p}, (1<p<\infty)$ sequence space. Several spectral subdivisions such as fine spectrum, discrete spectrum, essential spectrum, etc. are obtained. In addition, a few sufficient conditions on the absence of point spectrum over the essential spectrum are also discussed. |
| title | Spectrum and Fine Spectrum of Band Matrices Generated by Oscillatory Sequences |
| topic | Spectral Theory Functional Analysis Primary 47A10 (Primary), 47B37 (Secondary) |
| url | https://arxiv.org/abs/2301.09302 |