Timeline for Finite imensional subspaces of $L^\infty.$
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 20, 2012 at 19:48 | vote | accept | Igor Rivin | ||
| Apr 20, 2012 at 19:36 | comment | added | Bill Johnson | Greg said it right. Every centrally-symmetric polytope embeds isometrically into the much smaller space $c_0$; in fact, a finite dimensional Banach space embeds isometrically into $c_0$ if and only if its unit ball is a polytope. | |
| Apr 20, 2012 at 19:35 | comment | added | Greg Kuperberg | If a centrally symmetric $d$-polytope has $2n$ facets, then it is a slice of an $n$-cube, which also has $2n$ facets. You can construct the linear map directly from the hyperplanes of opposite pairs of facets. The word "obvious" doesn't do much for me, but let's say that it's an exercise. | |
| Apr 20, 2012 at 19:29 | comment | added | Igor Rivin | You mean "every centrally-symmetric polytope", I assume. Is that obvious? | |
| Apr 20, 2012 at 19:26 | history | answered | Greg Kuperberg | CC BY-SA 3.0 |