Krein Space Numerical Range of Block Matrices -- a Unified Approach to the Hyperbolic Case
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908492031328256 |
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| author | Bebiano, N. Lemos, R. Soares, G. |
| author_facet | Bebiano, N. Lemos, R. Soares, G. |
| contents | In this paper, we investigate the Krein space numerical range of $2$-by-$2$ block matrices, with diagonal blocks as scalar multiples of the identity. For these matrices, we specifically investigate the cases when the respective boundary generating curves consist of hyperbolas. This provides a unified approach to derive established and new results concerning the numerical range hyperbolic shape. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_12039 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Krein Space Numerical Range of Block Matrices -- a Unified Approach to the Hyperbolic Case Bebiano, N. Lemos, R. Soares, G. Functional Analysis 47A12, 15A60 In this paper, we investigate the Krein space numerical range of $2$-by-$2$ block matrices, with diagonal blocks as scalar multiples of the identity. For these matrices, we specifically investigate the cases when the respective boundary generating curves consist of hyperbolas. This provides a unified approach to derive established and new results concerning the numerical range hyperbolic shape. |
| title | Krein Space Numerical Range of Block Matrices -- a Unified Approach to the Hyperbolic Case |
| topic | Functional Analysis 47A12, 15A60 |
| url | https://arxiv.org/abs/2508.12039 |