Timeline for Embedding finite dimensional subspaces of Schatten p-classes
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 18, 2022 at 4:59 | vote | accept | Sijie Luo | ||
| May 16, 2022 at 6:26 | comment | added | Sijie Luo | Thank you very much for your kind suggestions, Prof. Johnson. In Section 3 of ”Three observations...” , Schechtman shown that only if $n\geq D^{\frac{-2p}{|p-2|k}}$, $l_{p}^{k}$ can be linearly embedded into $C_{p}^{n}$ with distortion at most $D$. This result is quite related to my question. However, I prefer to look for investigations of the following specific problem: Given $\varepsilon>0$ and $n$-dimensional subspace $X\subseteq C_{p}$, what is the smallest $N(\varepsilon,n)$ such that there exists a subspace $Y\subseteq C_{p}^{N(\varepsilon,n)}$ such that $d_{B-M}(X, Y)<1+\varepsilon$? | |
| May 12, 2022 at 20:19 | history | answered | Bill Johnson | CC BY-SA 4.0 |