Reference request: Kadec-Klee property for $\ell^1$

I am looking for references (textbooks or articles) where it is shown that the Banach space $\ell^1$ has the Kadec–Klee property, i.e. that the weak topology and the norm topology coincide on the unit sphere. Any recommended books, papers, or lecture notes that explicitly address this topological aspect would be greatly appreciated. I also welcome your own proofs or insights into why these two topologies coincide on the sphere in $\ell^1$.