I have been looking on the internet for hours now and even asking in chat without an answer. When is a set $M\subseteq\ell^2$ compact? For $L^p$, there is the Arzelà–Ascoli theorem that provides a useful tool, but I dont know how you can transfer it to $\ell^2$? Are there any similar theorems?
There is the following characterization:
$S\subset \ell^2$ is compact if and only the following conditions are satisfies: