About smooth and non-poor subspaces of Daugavet spaces
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918470076071936 |
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| author | Hamad, Samir |
| author_facet | Hamad, Samir |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_24529 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | About smooth and non-poor subspaces of Daugavet spaces Hamad, Samir Functional Analysis 46B04, 46B20, 46G05 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. |
| title | About smooth and non-poor subspaces of Daugavet spaces |
| topic | Functional Analysis 46B04, 46B20, 46G05 |
| url | https://arxiv.org/abs/2604.24529 |