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arXiv · 1706.05708

Roberts orthogonality and the Davis-Wielandt shell

Ljiljana Arambašić·Tomislav Berić·Rajna Rajić
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Abstract

Let $\mathcal A$ be a unital $C^*$-algebra with the unit $e$. We consider the elements $a\in \mathcal A$ which are Roberts orthogonal to the unit $e$. We obtain a characterization of this orthogonality in terms of the Davis--Wielandt shell of $a$ and show that, for certain classes of elements of $\mathcal A$, the Roberts orthogonality of $a$ and $e$ is equivalent to the symmetry of the numerical range of $a$ with respect to the origin.

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Ljiljana Arambašić, Tomislav Berić, Rajna Rajić. 2017-06-18. Roberts orthogonality and the Davis-Wielandt shell. https://arxiv.org/abs/1706.05708

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