Talk:Weakly Convergent Sequence in Normed Vector Space is Bounded

Topological duals of normed spaces are always Banach spaces yes. I will see if we have the result to point this out specifically. This is a specific case of the result that $\map B {X, Y}$ is Banach for NVSs $X$ and $Y$ if $Y$ is. Here $Y$ is either $\mathbb R$ or $\mathbb C$ both Banach. Caliburn (talk) 13:49, 18 September 2022 (UTC)

Yes, I found only this Space of Bounded Linear Transformations is Banach Space--Usagiop (talk) 14:08, 18 September 2022 (UTC)