Gelfand numbers of embeddings of schatten classes

Let 0<p,q≤∞ and denote by SNp and SNq the corresponding Schatten classes of real N×N matrices. We study the Gelfand numbers of natural identities SNp↪SNq between Schatten classes and prove asymptotically sharp bounds up to constants only depending on p and q. This extends classical results for finite-dimensional ℓp sequence spaces by E. Gluskin to the non-commutative setting and complements bounds previously obtained by B. Carl and A. Defant, A. Hinrichs and C. Michels, and J. Chávez-Domínguez and D. Kutzarova.