Timeline for What is the smallest Lipschitz constant of a Lipschitz retraction of $\ell_\infty([0,1])$ onto $C[0,1]$?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Jun 25, 2021 at 23:51 | history | suggested | jlewk | CC BY-SA 4.0 |
link leads to 404.
|
| Jun 25, 2021 at 22:22 | review | Suggested edits | |||
| S Jun 25, 2021 at 23:51 | |||||
| Apr 22, 2018 at 16:22 | comment | added | Taras Banakh | @FedorPetrov The constant 20 appears in the book of Benyamini and Lindenstrauss, where they construct a uniformly continuous retraction of $\ell_\infty(K)$ onto $C(K)$ which is locally Lipschitz with constant 20 at a neighborhood of $C(K)$ in $\ell_\infty(K)$. But even this local constant 20 cannot be traced to give a reasonable global Lipschitz constant. So the result of Kalton is very nice and exact (2 cannot be further improved). | |
| Apr 22, 2018 at 16:05 | comment | added | Tomasz Kania | @FedorPetrov, I think it simply the estimate that follows from the Lindenstrauss' (non-optimal) proof. Kalton wanted to make a case that his result indeed strengthens the original result. | |
| Apr 22, 2018 at 16:04 | comment | added | Fedor Petrov | On the first page of this paper the constant 20 (by Lindenstrauss) is mentioned. It is the same as was asked by OP. May I wonder, is it something special to have Lipschitz constant 20? | |
| Apr 22, 2018 at 16:01 | comment | added | Tomasz Kania | @TarasBanakh, you are most welcome. I remember that I had used this result some time ago. | |
| Apr 22, 2018 at 16:00 | vote | accept | Taras Banakh | ||
| Apr 22, 2018 at 15:57 | history | answered | Tomasz Kania | CC BY-SA 3.0 |