Timeline for Schauder basis $L^p(\mathbb{R})$
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 4, 2018 at 13:08 | comment | added | Bill Johnson | A uniformly bounded orthonormal system that is unconditional in $L^p$ must be equivalent to the unit vector basis of $\ell^2$ (e.g., use type-ecotype theory), so a basis of characters cannot be unconditional. Therefore there is a permutation of any character basis for $L^p$ that is not a basis for $L^p$ when $p\not=2$. | |
| Jan 3, 2018 at 23:19 | comment | added | Fedor Petrov | Trigonometric system is a Schauder basis for all $L^p,p>1$. Probably we may check other specific example like Walsh. | |
| Jan 3, 2018 at 21:38 | comment | added | Nebojša Đurić | And for some p>1? | |
| Jan 3, 2018 at 21:06 | history | answered | Fedor Petrov | CC BY-SA 3.0 |