Structural properties of 2-C-normal operators
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911198313709568 |
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| author | Guesba, Messaoud Lakehal, Ismail Mahmoud, Sid Ahmed Ould Ahmed |
| author_facet | Guesba, Messaoud Lakehal, Ismail Mahmoud, Sid Ahmed Ould Ahmed |
| contents | In this paper, we introduce and study a new class of bounded linear operators on complex Hilbert spaces, which we call 2-C-normal operators. This class is inspired by and closely related to the notion of 2-normal operators, with additional structure imposed via conjugation. We investigate various fundamental properties of 2-C-normal operators, including algebraic characterizations, spectral properties, and examples that distinguish them from classical normal and 2-normal operators. Additionally, we explore how this class behaves under common operator transformations and examine its relation to other well-studied families of operators. The results presented contribute to a deeper understanding of conjugation-influenced operator behavior and open avenues for further study in the context of complex symmetric operator theory. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_06883 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Structural properties of 2-C-normal operators Guesba, Messaoud Lakehal, Ismail Mahmoud, Sid Ahmed Ould Ahmed Functional Analysis In this paper, we introduce and study a new class of bounded linear operators on complex Hilbert spaces, which we call 2-C-normal operators. This class is inspired by and closely related to the notion of 2-normal operators, with additional structure imposed via conjugation. We investigate various fundamental properties of 2-C-normal operators, including algebraic characterizations, spectral properties, and examples that distinguish them from classical normal and 2-normal operators. Additionally, we explore how this class behaves under common operator transformations and examine its relation to other well-studied families of operators. The results presented contribute to a deeper understanding of conjugation-influenced operator behavior and open avenues for further study in the context of complex symmetric operator theory. |
| title | Structural properties of 2-C-normal operators |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2510.06883 |