论文标题
schatten类的嵌入数字
Gelfand numbers of embeddings of Schatten classes
论文作者
论文摘要
令$ 0 <p，q \ leq \ infty $，并用$ \ mathcal {s} _p^n $和$ \ mathcal {s} _q^n $表示真实$ n \ times n $矩阵的相应schatten类。我们研究了gelfand的自然身份数量$ \ MATHCAL {s} _p^n \ hookrightarrow \ Mathcal {s} _Q^n $之间的Schatten类之间，并且仅根据$ p $和$ q $而证明仅渐近地与常数界限。这将E. Gluskin的有限维$ \ ell_p $序列空间的经典结果扩展到了非交通设置，并补充了B. Carl和A. Defant，A。Hinrichs和C. Michels和J.Chávez-Domínguez和D. Kutzarova先前获得的边界。
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. Chávez-Domínguez and D. Kutzarova.
