The Fréchet spaces ces(p+),1 < p < ∞

The Banach spaces ces(p),1pℓq into itself. It is shown that the largest solid Fréchet lattice in CN which contains ℓp+ and which C maps into ℓp+ is precisely ces(p+):=⋂q>pces(q). Although the spaces ℓp+ are well understood, it seems that the spaces ces(p+) have not been considered at all. A detailed study of the Fréchet spaces ces(p+),1≤p<∞, is undertaken. They are very different to the Fréchet spaces ℓp+ which generate them in the above sense. We prove that each ces(p+) is a power series space of finite type and order one, and that all the spaces ces(p+),1≤p<∞, are isomorphic.