On analytic functions into $l^{p}$-spaces

Abstract:

Let $\Delta$ be the open unit disc in the complex plane and let $1 \leqslant p < \infty$. We construct an example of a discontinuous function from $\Delta$ into ${l^p}$ which is analytic as a function from $\Delta$ into ${l^{p’}}$ for any $p’ > p$ and whose derivatives (into ${l^{p’}}$) of all orders are functions into ${l^p}$.