# Is the set of compact operators on a complex infinite dimensional Hilbert space compact?

Let $$\mathbb{H}$$ be a complex infinite dimensional Hilbert space and $$B \left( \mathbb{H} \right)$$ bes the algebra of bounded linear operators on $$\mathbb{H}$$.

I would like to find a compact subset of $$B \left( \mathbb{H} \right)$$.

One of the candidate is the set of all compact operators since it is closed. Is the set of all compact operators on $$B \left( \mathbb{H} \right)$$ ?

Otherwise, could you please let me know another possibility?