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Let $0<p,qleq infty$ and denote by $mathcal{S}_p^N$ and $mathcal{S}_q^N$ the corresponding Schatten classes of real $Ntimes N$ matrices. We study the Gelfand numbers of natural identities $mathcal{S}_p^Nhookrightarrow mathcal{S}_q^N$ 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. Chavez-Dominguez and D. Kutzarova.
Let $0<p,qleq infty$ and denote by $mathcal S_p^N$ and $mathcal S_q^N$ the corresponding Schatten classes of real $Ntimes N$ matrices. We study approximation quantities of natural identities $mathcal S_p^Nhookrightarrow mathcal S_q^N$ between Schatte
In this paper we will study the asymptotic behaviour of certain widths of the embeddings $ mathcal{A}_omega(mathbb{T}^d) to L_p(mathbb{T}^d)$, $2le p le infty$, and $ mathcal{A}_omega(mathbb{T}^d) to mathcal{A}(mathbb{T}^d)$, where $mathcal{A}_{omega
We establish the necessary and sufficient conditions for those symbols $b$ on the Heisenberg group $mathbb H^{n}$ for which the commutator with the Riesz transform is of Schatten class. Our main result generalises classical results of Peller, Janson-
We study the embedding $text{id}: ell_p^b(ell_q^d) to ell_r^b(ell_u^d)$ and prove matching bounds for the entropy numbers $e_k(text{id})$ provided that $0<p<rleq infty$ and $0<qleq uleq infty$. Based on this finding, we establish optimal dimension-fr
The Thompson metric provides key geometric insights in the study or non-linear matrix equations and in many optimization problems. However, knowing that an approximate solution is within d_T units of the actual solution in the Thompson metric provide