Timeline for Renorming of $C[0,1]$ for a strictly convex dual
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 6, 2020 at 2:42 | vote | accept | Tanmoy Paul | ||
| Jun 29, 2020 at 15:58 | comment | added | Tanmoy Paul | My earlier question can be reformulated as follows. Does there exist an equivalent renorming on $C[0,1]$ which makes it (weakly) Hahn-Banach smooth? Probably the answer to this problem is 'No' because the dual of any weakly Hahn-Banach smooth space has RNP. | |
| Jun 29, 2020 at 15:55 | comment | added | Tanmoy Paul | Thank you Jochen for pointing out. I was a bit confused about Hahn-Banach smoothness and smoothness. A Banach space $X$ is said to be Hahn-Banach smooth if every $x^*\in X^*$ has unique norm preserving extension to $X^{**}$. Similarly a weaker version of this property can also be defined for the norm attaining functionals. If $X^*$ is strictly convex then any subspace of $X$ is Hahn-Banach smooth BUT this property does not imply (weakly) Hahn-Banach smoothness of $X$. | |
| Jun 29, 2020 at 13:31 | answer | added | Bill Johnson | timeline score: 7 | |
| Jun 29, 2020 at 8:12 | comment | added | Jochen Wengenroth | The dual of every separabel Banach space has an eqivalent strictly convex norm, but I understand that this is not you question. | |
| Jun 29, 2020 at 7:03 | history | asked | Tanmoy Paul | CC BY-SA 4.0 |