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arXiv · 2609.27693

Characterizing the Daugavet property by squares of rank-one operators

Johann Langemets
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Abstract

We prove that, for real Banach spaces of dimension greater than one, each of the identities $\|Id+T^2\|=1+\|T^2\|$ and $\|Id-T^2\|=1+\|T^2\|$, required for every rank-one operator $T$, characterizes the Daugavet property, thereby answering a question posed by Kadets, Martín, and Merí (2007). Consequently, every extremely non-complex Banach space of dimension greater than one has the Daugavet property, answering a question of Martín and Merí (2011). We also compare pointwise versions of the square Daugavet properties with Daugavet points, $Δ$-points, and $\nabla$-points.

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Johann Langemets. 2026-09-23. Characterizing the Daugavet property by squares of rank-one operators. https://arxiv.org/abs/2609.27693

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