Hello! At the moment I'm preparing for an exam, and I'm stuck trying to answear the following (any suggestions are welcome):

Let H be a Hilbert space and denote by L(H) the space of all continuous linear maps from H to H (L(H) a Banach space). Suppose that the dimension of our H is infinite. Is L(H) separable? Why?

I'm thinking it's not. However, I've got nothing but intuition to back that up with.