Properties of interpolation spaces of completely continuous operators

We consider interpolation spaces $\mathfrak G_{\theta,p}$ between the space $\mathfrak G_1$of nuclear operators and the space $\mathfrak G_\infty$ of completely continuous operators in a Hilbert space. We obtain an exact expression for the norm of an operator of $\mathfrak G_{\theta,p}$ by means of its approximation numbers. We consider the question of separability of the symmetric normed ideals of $\mathfrak G_{\theta,p}$, and the question of the duals to these s.n. ideals.