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arXiv · 2604.24529

About smooth and non-poor subspaces of Daugavet spaces

Samir Hamad
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Abstract

We discuss an example of a non-complete normed space with the Daugavet property such that the norm is Gâteaux differentiable at every nonzero point. In contrast, we note that the dual norm of a normed space with the Daugavet property is not Gâteaux differentiable at any point. Furthermore, we show that quasilacunary Müntz spaces form a natural class of subspaces of $C[0,1]$, isomorphic to $c_0$, for which the corresponding quotient spaces fail to have the Daugavet property. At the same time, the slice diameter two property is preserved under this construction.

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Samir Hamad. 2026-04-27. About smooth and non-poor subspaces of Daugavet spaces. https://arxiv.org/abs/2604.24529

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