Timeline for Hahn Banach type extension of a Lipschitz map
Current License: CC BY-SA 3.0
16 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 4, 2018 at 6:05 | vote | accept | Tanmoy Paul | ||
| Sep 18, 2017 at 10:24 | comment | added | M A Sofi | Lipschitz maps defined on subspaces of Hilbert spaces and taking values in an arbitrary Banach space extend to Lipschitz maps (with the same Lipschitz constant) on the whole space. However, I shall deeply appreciate to know if the result extends to type 2 Banach space in place of Hilbert spaces, this time with the mappings also taking values in a Hilbert space. The linear analogue of this statement, with linear maps being used in place of Lipschitz maps is a well known theorem of B. Maurey. | |
| Jul 26, 2015 at 16:06 | answer | added | Nik Weaver | timeline score: 11 | |
| Jul 26, 2015 at 15:55 | comment | added | Yemon Choi | I suggest that you "unaccept" the answer below, otherwise people will think that your question has been fully answered and move on without looking | |
| Jul 26, 2015 at 15:04 | history | reopened |
Joonas Ilmavirta Daniel Moskovich Yemon Choi Johannes Hahn Will Sawin |
||
| Jul 26, 2015 at 13:00 | history | edited | Johannes Hahn | CC BY-SA 3.0 |
Removed abbreviations, fixed laxout, added tags
|
| Jul 26, 2015 at 11:48 | vote | accept | Tanmoy Paul | ||
| Jul 26, 2015 at 16:03 | |||||
| Jul 26, 2015 at 9:59 | review | Reopen votes | |||
| Jul 26, 2015 at 15:05 | |||||
| Jul 26, 2015 at 9:42 | history | edited | Tanmoy Paul | CC BY-SA 3.0 |
a precise problem related to my earlier question is mentioned.
|
| Jul 26, 2015 at 6:48 | comment | added | Tanmoy Paul | I knew only about the result by Kirszbrzun but not any further development.Here is what I would like to ask.Let $X$ be a real Banach sp,$Y$ a subspace of it and $f$ a 1-Lip map from $X$ to $\mathbb{R}$.Is it possible to get an extn of $f$ from $X$ to $\mathbb{R}$ with Lip constant 1? The case when $X$ is a metric sp and $Y$ a finite dim. subsp, the result follows from MR0737400(86a:46018).But let us assume $X=C(K)$,$K$ is cpt $T_2$(can assume metrizable also)and $Y=\{f:f|_D=0\}$ (ie an M-ideal) of $X$.Now can a real valued 1-Lip map from $Y$ necessarily has a similar extn ? Can it be unique ? | |
| Jul 25, 2015 at 20:51 | history | closed |
Marco Golla Stefan Kohl♦ Alex Degtyarev Bill Johnson Joonas Ilmavirta |
Needs details or clarity | |
| Jul 25, 2015 at 18:05 | comment | added | Tanmoy Paul | Okay, I mean a metrizable lctvs but not necessarily normed linear space. | |
| Jul 25, 2015 at 17:00 | review | Close votes | |||
| Jul 25, 2015 at 20:51 | |||||
| Jul 25, 2015 at 16:28 | comment | added | Nik Weaver | The question doesn't make sense --- there is no notion of distance in an LCTVS. | |
| Jul 25, 2015 at 16:03 | review | First posts | |||
| Jul 25, 2015 at 16:43 | |||||
| Jul 25, 2015 at 15:56 | history | asked | Tanmoy Paul | CC BY-SA 3.0 |