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arXiv · 2407.13861

On the reduction of powers of self-adjoint operators

Salima Kebli·Mohammed Hichem Mortad
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Abstract

Let $T\in B(H)$ be such that $T^n$ is self-adjoint for some $n\in\mathbb{N}$ with $n\geq 3$. The paper's primary aim is to establish the conditions that lead to the self-adjointness of $T$. We pay particular attention to the case where $T^3=0$ and how it implies $T$ is complex symmetric.

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Salima Kebli, Mohammed Hichem Mortad. 2024-07-18. On the reduction of powers of self-adjoint operators. https://arxiv.org/abs/2407.13861

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