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 ${\mathrm{\ell }}^1$ while noticing that every separable subspace of $L^{\mathrm{\infty }}[0,1]$ is poor.