Let $H$ be a separable Hilbert space and $K(H)$ the Banach space of all compact linear maps from $H$ into itself (with the operator norm).
Show that $K(H)$ is separable.
There is a hint that states that I should find a countable set of compact symmetric linear maps that is dense in the set of all compact symmetric linear maps.
Any hints on how to show this? Is the set of all compact symmetric linear maps dense in $K(H)$?
Alternatively, is it possible to utilize the result here?