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arXiv · 2610.39080

Additive preservers of mutual strong numerical radius orthogonality

Yulong Tian·Jinli Xu
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Abstract

Let $H$ be a complex Hilbert space with $\dim H\ge2$. We show that the additive surjections on $\mathcal{B}(H)$ and on its self-adjoint part $\mathcal{B}_s(H)$ that preserve mutual strong numerical-radius orthogonality in one direction are precisely the maps of the form $A\mapsto cUAU^*$, where $U$ is a unitary or antiunitary operator on $H$ and $c$ is a nonzero complex or real scalar, respectively.

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Yulong Tian, Jinli Xu. 2026-10-29. Additive preservers of mutual strong numerical radius orthogonality. https://arxiv.org/abs/2610.39080

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