Gelfand numbers of embeddings of Schatten classes

Let $$0<p,q\le \infty $$ and denote by $$\mathscr {S}_p^N$$ {S}_q^N$$ the corresponding Schatten classes of real $$N\times N$$ matrices. We study Gelfand numbers natural identities {S}_p^N\hookrightarrow \mathscr between prove asymptotically sharp bounds up to constants only depending on p q. This extends classical results for finite-dimensional $$\ell _p$$ sequence spaces E. Gluskin non-commutative setting complements previously obtained B. Carl A. Defant, Hinrichs C. Michels, J. Chávez-Domínguez D. Kutzarova.