Let $X$,$Y$ be normed spaces, and $\mathcal B(X,Y)$ be the space ob bounded linear operators from $X$ to $Y$. Then $\mathcal B(X,Y)$ is a normed space. Denote be $\overline{\mathcal B(X,Y)}$ its completion.
What elements are in this completion, are they still operators from $X$ to $Y$?
I think $\overline{\mathcal B(X,Y)}$ should be isomorphic to $\mathcal B(X,\overline Y)$, is it true?