Measures of weak non-compactness in spaces of nuclear operators

We show that in the space of nuclear operators from ${\mathrm{\ell }}^q(\mathrm{\Lambda })$ to ${\mathrm{\ell }}^p(J)$ the two natural ways of measuring weak non-compactness coincide. We also provide explicit formulas for these measures. As a consequence the same is proved for preduals of atomic von Neumann algebras.