Timeline for Geometric implications of $\beta(B_X) = 2$
Current License: CC BY-SA 3.0
19 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 10, 2016 at 11:25 | history | edited | anonymous | CC BY-SA 3.0 |
Pull in some more info. Ready for the archive.
|
| Dec 8, 2016 at 15:12 | history | edited | anonymous | CC BY-SA 3.0 |
Add an examples for C[0,1]
|
| Dec 8, 2016 at 15:02 | history | edited | anonymous | CC BY-SA 3.0 |
Add a note about why reflexivity is important
|
| Dec 8, 2016 at 6:47 | vote | accept | anonymous | ||
| Dec 7, 2016 at 21:00 | answer | added | Bunyamin Sari | timeline score: 2 | |
| Dec 7, 2016 at 16:16 | history | edited | anonymous | CC BY-SA 3.0 |
Mention upper bound on lower bound for non-reflexive spaces
|
| Dec 7, 2016 at 16:08 | history | edited | anonymous | CC BY-SA 3.0 |
Mention lower bound on non-reflexive spaces
|
| Dec 7, 2016 at 16:01 | comment | added | anonymous | One has $\beta(B_{\ell^p}) = 2^{1/p}$ for $1 \le p < \infty$. Thus, $\lim_{p \to \infty} \beta(B_{\ell^p}) = 1$, but $\beta(B_{\ell^\infty}) = 2$. | |
| Dec 7, 2016 at 15:48 | history | edited | anonymous | CC BY-SA 3.0 |
We're only interested in infinite-dimensional spaces here.
|
| Dec 7, 2016 at 15:46 | comment | added | anonymous | @Dirk It is shown in the article by Elton and Odell which Bill Johnson has just mentioned (available e.g. from eudml.org/doc/266720) that $\beta(B_X)$ is always strictly greater than 1. | |
| Dec 7, 2016 at 15:32 | answer | added | Bill Johnson | timeline score: 1 | |
| Dec 7, 2016 at 15:26 | comment | added | Dirk | Oh, interesting. Another notion of "roundness" is the modulus of convexity. | |
| Dec 7, 2016 at 15:23 | history | edited | anonymous | CC BY-SA 3.0 |
Add more questions
|
| Dec 7, 2016 at 15:07 | comment | added | anonymous | @Dirk I'm not actually sure if such spaces exist. I've now added examples that show $\beta(B_X) = 2$ also for $\ell^1$ and $L^1[0,1]$. Maybe $\sqrt 2$ is actually the minimal value for $\beta(B_X)$. | |
| Dec 7, 2016 at 15:05 | history | edited | anonymous | CC BY-SA 3.0 |
Complete distinction of cases
|
| Dec 7, 2016 at 14:40 | history | edited | anonymous | CC BY-SA 3.0 |
Clearer notation
|
| Dec 7, 2016 at 14:26 | history | edited | anonymous | CC BY-SA 3.0 |
Add a note about $c_0$.
|
| Dec 7, 2016 at 14:10 | comment | added | Dirk | I have no idea, but out of curiosity: What are examples of $\beta(B_X) = 1$? I suspect that their unit balls are not round, either. | |
| Dec 7, 2016 at 14:00 | history | asked | anonymous | CC BY-SA 3.0 |