New posts in Weak Topology

If $Y\subset X$ are Banach spaces such that $Y$ is dense in $X$, is it true that $X'$ is dense in $Y'$?

Why are weak topologies useful in functional analysis?

In "Analyse fonctionnelle" of Brezis, in chapter III why do we need Banach spaces ? (especially for Kakutani's theorem)

Brezis Exercise 3.9