Completing the Valdivia-Vogt tables of sequence-space representations of spaces of smooth functions and distributions.

In the Valdivia-Vogt structure tables presented in Ortner and Wagner (J Math Anal Appl 404(1):1-10, ) there are two gaps. We fill in these gaps by proving the representations $$\mathcal {D}^{F}\cong s\widehat{\otimes }_{\pi }\mathbb {C}^{(\mathbb {N})}$$ and $$\dot{\mathcal {B}}' \cong s'\widehat{\otimes } c_{0}$$ , where $$\mathcal {D}^{F}$$ is a pre-dual space of the space of distributions of finite order introduced by J. Horváth and the space $$\dot{\mathcal {B}}'$$ is the space of distributions vanishing at infinity introduced by L. Schwartz. [ABSTRACT FROM AUTHOR]