A note on a theorem of Sparr - Ameur, Y. (MATHEMATICA SCANDINAVICA, 2004)
We prove that, regardless of the choice of a positive, concave function $ψ$ on $R_{+}$ and a "weight function" $λ$, the weighted $\ell_2$-space $\ell_2(ψ(λ))$ is $c$-interpolation with respect to the couple $(\ell_2,\ell_2(λ))$, where $c≤\sqrt{2}$. Our main result is that $c=\sqrt{2}$ is best possible here; a fact which is implicit in the work of G. Sparr.