Timeline for Relationship between $2 \to 2$ norm and $\infty \to 2$ norm
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Mar 21, 2019 at 9:11 | comment | added | InfiniteLooper | And by such not of research level. See MathSE for questions of this type. | |
| Mar 21, 2019 at 9:10 | comment | added | InfiniteLooper | Then take $x = (1, 0, \cdots, 0)$. The point is that your question is just on comparaison of classical norms in a finite dimensional real vector space. | |
| Mar 21, 2019 at 0:54 | comment | added | Alex Wenxin Xu | Sorry I meant to ask if the first inequality is tight | |
| Mar 19, 2019 at 12:46 | comment | added | Marcelo Ng | We can think about the behavior of $L^p \mapsto L^q$ operators, where $p = 2= q$ and $p = + \infty, q = 2$. For example $T(f) = f \varphi$ for a suitable $\varphi$. Thus, we can apply a interpolation theorem to compare the norms of theses operators. For example, the Riesz-Thorin theorem: en.wikipedia.org/wiki/Riesz%E2%80%93Thorin_theorem | |
| Mar 19, 2019 at 7:42 | history | answered | InfiniteLooper | CC BY-SA 4.0 |