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arXiv · 2510.06883

Structural properties of 2-C-normal operators

Messaoud Guesba·Ismail Lakehal·Sid Ahmed Ould Ahmed Mahmoud
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Abstract

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.

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BibTeXRIS

Messaoud Guesba, Ismail Lakehal, Sid Ahmed Ould Ahmed Mahmoud. 2025-10-08. Structural properties of 2-C-normal operators. https://arxiv.org/abs/2510.06883

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