Timeline for Banach-Mazur distance estimate finite-dimensional $\ell_p$ spaces
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| S Oct 17, 2013 at 10:50 | history | suggested | Davide Giraudo | CC BY-SA 3.0 |
improved formatting of the title.
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| Oct 17, 2013 at 10:00 | review | Suggested edits | |||
| S Oct 17, 2013 at 10:50 | |||||
| Oct 13, 2013 at 23:22 | comment | added | Bill Johnson | I am home now and checked that the result I mentioned is proved as Proposition II.E.8 in Wojtaszczyk's book "Banach spaces for analysts". For the upper estimate, he simply says that it is obvious by taking the identity operator (no hint about using Holder, I guess because what else can you do if it is obvious?). | |
| Oct 13, 2013 at 16:12 | comment | added | Ben W | Ah, okay thank you. And as for the problem, well, I'm just not quite as good at all this as some of you folks out there. I sometimes get hung up on trivial stuff like this. Not everyone has the brilliant mind of WBJ. ; ) | |
| Oct 13, 2013 at 15:39 | comment | added | Bill Johnson | I have trouble understanding what the problem is. The distance from $\ell_p^n$ to $\ell_2^n$ is $n^{|1/p-1/2|}$ and is given by looking at the identity operator. The upper estimate, which is what you are seeking, is very easy from Holder's inequality. The harder part is to show that the identity map gives the minimum and this is surely in Tomczak's book (but I do not have a copy here to check). | |
| Oct 13, 2013 at 14:21 | history | asked | Ben W | CC BY-SA 3.0 |