Summing norms of identities between unitary ideals

Based on abstract interpolation, we prove asymptotic formulae for the (F, 2)-summing norm of inclusions id : S-E(n) --> S-2(n), where E and F are two Banach sequence spaces. Here, S-E(n) stands for the unitary ideal of operators on the n-dimensional Hilbert space whose singular values belong to E, and S-2(n) = S-l2(n) for the Hilbert-Schmidt operators. Our results are noncommutative analogues of results due to Bennett and Carl, as well as their recent generalizations to Banach sequence spaces. As an application, we give lower and upper estimates for certain s-numbers of the embeddings id : S-E(n) --> S-2(n) and id : S-2(n) --> S-E(n). In the concluding section, we finally consider mixing norms.