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arXiv · 2011.06554

Gelfand numbers of embeddings of Schatten classes

Aicke Hinrichs·Joscha Prochno·Jan Vybíral
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Abstract

Let $0<p,q\leq \infty$ and denote by $\mathcal{S}_p^N$ and $\mathcal{S}_q^N$ the corresponding Schatten classes of real $N\times N$ matrices. We study the Gelfand numbers of natural identities $\mathcal{S}_p^N\hookrightarrow \mathcal{S}_q^N$ between Schatten classes and prove asymptotically sharp bounds up to constants only depending on $p$ and $q$. This extends classical results for finite-dimensional $\ell_p$ 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. Ch\'avez-Dom\'inguez and D. Kutzarova.

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Aicke Hinrichs, Joscha Prochno, Jan Vybíral. 2020-11-12. Gelfand numbers of embeddings of Schatten classes. https://arxiv.org/abs/2011.06554

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