What would be an easy example of a bijective continuous map between Banach spaces whose inverse is not continuous?
A usual example of a bijective continuous function between metric spaces would be $f(x)=x^2$ on $(-1,0]\cup[1,2]$, where $f^{-1}$ does map the connected set $[0,4]$ to the unconnected set $(-1,0]\cup[1,2]$ and hence is not continuous.
But I fail to come up with an example, where the domain and range are Banach spaces.