Timeline for Ultraproduct of n-dimensional Banach spaces and algebras
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 6, 2011 at 21:37 | vote | accept | Kent Vollenweider | ||
| Jul 6, 2011 at 15:04 | comment | added | Matthew Daws | @Juris-- But then the "correct" unit length basis vectors also become enlongated, and so the distortions sort of cancel out... | |
| Jul 6, 2011 at 12:58 | comment | added | Juris Steprans | Thanks Matthew. I had had in mind a sequence of 2-dimensional spaces with increasingly oblong unit balls. I will have to think about why the bounded Banach-Mazur distance saves the day for such a product. | |
| Jul 6, 2011 at 12:37 | comment | added | Matthew Daws | The condition on your second paragraph is always true, as a k-dim Banach space is always at most $\sqrt{k}$ distant from $\ell^2_k$ in the Banach-Mazur distance-- see en.wikipedia.org/wiki/Banach%E2%80%93Mazur_compactum | |
| Jul 6, 2011 at 12:01 | history | answered | Juris Steprans | CC BY-SA 3.0 |