Timeline for Can you tell whether a space is Banach from the unit ball?
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 3, 2011 at 4:42 | vote | accept | Jim Belk | ||
| Mar 3, 2011 at 4:42 | |||||
| Mar 1, 2011 at 4:19 | comment | added | Deane Yang | Bill, I did wonder a bit whether the question was just a homework problem. | |
| Feb 28, 2011 at 21:00 | comment | added | Bill Johnson | Take $B$ to be the closed unit ball of the Minkowski functional for $B$. The usual way of checking that the normed space that has $B$ as the unit ball is complete is to verify that $B$ is closed in some Banach space that contains $B$ s.t the unit ball of the Banach space contains $B$. You can find this as an exercise in some books (not that I recall which ones). | |
| Feb 28, 2011 at 20:00 | comment | added | Pietro Majer | Thank you, I was wondering if I had to expand the comment, with the same remark ;-) Also note that for the completeness of a normed space it it sufficient the convergence of all geometric series, that is with $|x_n|\leq 2^{-n}$ | |
| Feb 28, 2011 at 19:50 | comment | added | Matthew Daws | Edit: While I typed this, Pietro make a comment. Of course, all I've done is actually carry out Pietro's comment more explicitly... | |
| Feb 28, 2011 at 19:49 | history | answered | Matthew Daws | CC BY-SA 2.5 |