Timeline for Idiosyncratic characterizations of $\ell^p$, for $p\not=1,2,\infty$
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| May 30, 2014 at 0:49 | comment | added | Norbert | In fact there is nothing special in Littlewood's inequality. It is a manifistation of general result of Kwapien: any operator from $\mathcal{L}_1$ space to $\mathcal{L}_p$ space is $(r,1)$-summing for $r^{-1}=1-|p^{-1}-2^{-1}|$ and $p>1$. For details see page 208 in Absolutely Summing Operators by Joe Diestel | |
| Jun 27, 2013 at 14:57 | history | edited | Andrey Rekalo | CC BY-SA 3.0 |
fixed LaTex
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| Dec 13, 2010 at 17:15 | comment | added | Andrey Rekalo | Dear Willie, many thanks for your comment. | |
| Dec 13, 2010 at 16:54 | comment | added | Willie Wong | Dear Andrey: I got confused by where you put the if and only if. Sorry. Deleted the irrelevant comments. | |
| Dec 13, 2010 at 14:38 | history | edited | Andrey Rekalo | CC BY-SA 2.5 |
Example 2 is added.
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| Dec 13, 2010 at 12:25 | comment | added | Willie Wong | Also, if you use the higher dimensional version by Bohnenblust and Hille, you can also similarly characterize all numbers $p = \frac{2m}{m+1}$ for $m\in \mathbb{N}$. (The inequality is $$ \|\hat{a}\|_{\ell^p(\mathbb{N}^m)} \leq 2^{(m-1)/2} \|\hat{a}\| $$ where on the RHS is $\sup \hat{a}(x_1,\ldots,x_m)$ with each $x_i\in \ell^\infty(\mathbb{N})$.) | |
| Dec 13, 2010 at 7:51 | comment | added | David Feldman | Interesting, and close to what I want, but this doesn't so much single out the space $\ell^{4/3}$ as single out the number $4/3$. If it could be combined with a condition characterizing $\ell^p$'s for $p\leq 4/3$, that would be perfect. | |
| Dec 13, 2010 at 7:13 | history | edited | Andrey Rekalo | CC BY-SA 2.5 |
added 352 characters in body
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| Dec 13, 2010 at 6:53 | history | answered | Andrey Rekalo | CC BY-SA 2.5 |