发表机构
Institute of Mathematics and Statistics, University of Tartu（塔尔图大学数学与统计研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明维数大于1的实巴拿赫空间中秩一算子平方的范数恒等式可刻画Daugavet性质，并回答了两个开放问题，同时比较了相关逐点概念。
AI 中文摘要
我们证明，对于维数大于1的实巴拿赫空间，对每个秩一算子T，恒等式‖Id+T²‖=1+‖T²‖和‖Id-T²‖=1+‖T²‖各自都能刻画Daugavet性质，从而回答了Kadets、Martín和Merí（2007）提出的一个问题。因此，每个维数大于1的极非复巴拿赫空间都具有Daugavet性质，回答了Martín和Merí（2011）的一个问题。我们还比较了平方Daugavet性质的逐点版本与Daugavet点、Δ点和∇点。
英文摘要
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.
