A note on isomorphisms between powers of Banach spaces

We are concerned with the following problem: "Let $E$ and $F$ be Banach spaces such that $E^I$ is isomorphic to $F^I$ for some infinite set $I$. Then, when does it follow that $E$ is isomorphic to $F$?". Here, we provide a partial answer to this problem and characterize the Banach spaces $E$ which are isomorphic to any $F$ whenever $F^\mathbb{N}$ is isomorphic to $E^\mathbb{N}$