arXiv subjects

Samir Hamad

Publications and source records attributed to Samir Hamad.

4 recordsLinked to original sources

arXiv2026

Tensor Products and the Isomorphic Theory of Daugavet Spaces

We construct two separable Banach spaces with the Daugavet property whose injective and projective tensor squares, respectively, fail the Daugavet property. Both examples arise from one sequence of finite-dimensional extensions. The first space is the completion of the increasing union of the extensions, whereas the second is the closed span of their coordinate functionals. We will also investigate the operator Daugavet properties of these spaces later in the paper, also highlighting natural examples of metric spaces $M$ for which $\operatorname{Lip}_0(M)$ has the Daugavet property but fails to have the weak operator Daugavet property. Independently of this, we will also prove that every Banach space admits a linear isometric embedding into a Banach space which is not isomorphic to any Banach space with the Daugavet property.

math.FA↗

arXiv2026

On the weak operator Daugavet property and poor subspaces

We will provide an example of a Banach space with the Daugavet property which does not possess the weak operator Daugavet property. We will also show that every separable Banach space with the Daugavet property contains a non-poor subspace isomorphic to $\ell^1$ while noticing that every separable subspace of $L^\infty[0,1]$ is poor.

math.FA↗

arXiv2026

About smooth and non-poor subspaces of Daugavet spaces

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.

math.FA↗

arXiv2026

The Daugavet property for Sobolev spaces over the plane

We show that $W^{1,1}(\mathbb{R}^2)$ has the Daugavet property when endowed with the norm induced by the $L^1$-norm of the gradient, but fails to have the slice diameter two property when equipped with the usual Sobolev norm.

math.FA↗