If we have a Hilbert space $H$, (so it is reflexive) then by Banach-Alaoglu's theorem, the closed unit ball $B\subset H$ is weakly-compact. My question is,
Is there any corollary or similar theorem or conditions that gives compactness? I mean, some ingredient or condition that shows that the unit ball of a Hilbert space is compact?
Thank you very much for your help! :)