$\ell^1$ Schur property
As Giusepped pointed out in the comments, the problem is that $f$ is not a priori the same for each $n$.
Here are the ideas for a proof of the Schur property.
As Giusepped pointed out in the comments, the problem is that $f$ is not a priori the same for each $n$.
Here are the ideas for a proof of the Schur property.