Timeline for Subspace of $L^2$ that lies in $L^\infty$
Current License: CC BY-SA 2.5
16 events
| when toggle format | what | by | license | comment | |
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| Jul 9, 2018 at 16:33 | comment | added | Bart Michels | Also see Borel, Automorphic forms on SL2(R), Lemma 8.3, where it is stated that this result is due to Godement. | |
| Jul 10, 2017 at 19:56 | comment | added | Pietro Majer | Also check problem 349 of Bernard Gelbaum's Problems in Analysis (Springer 1982) , chapter on Hilbert spaces, where it is also shown by elementary inequalities: "If $\|f\|_\infty\le C\|f\|_2$ for all $f\in M$, $M$ a subspace of $L^2([0,1])$, then $\rm{dim}(M)\le C^2$". | |
| Jan 20, 2011 at 1:46 | comment | added | Yemon Choi | Since it seems that using the open mapping theorem is allowed, perhaps the reference to Rudin might still be of interest? It's Theorem 5.2 in Functional Analysis (2nd ed) | |
| Jan 19, 2011 at 19:12 | comment | added | Yemon Choi | Sorry, I left a reference (to Rudin's book) as an answer without properly reading your question, and in particular the fact that you wanted a proof avoiding functional-analytic tricks | |
| Jan 19, 2011 at 18:44 | vote | accept | Rostyslav Kravchenko | ||
| Jan 19, 2011 at 17:50 | vote | accept | Rostyslav Kravchenko | ||
| Jan 19, 2011 at 17:57 | |||||
| Jan 19, 2011 at 16:24 | vote | accept | Rostyslav Kravchenko | ||
| Jan 19, 2011 at 16:28 | |||||
| Jan 19, 2011 at 16:24 | vote | accept | Rostyslav Kravchenko | ||
| Jan 19, 2011 at 16:24 | |||||
| Jan 19, 2011 at 16:24 | vote | accept | Rostyslav Kravchenko | ||
| Jan 19, 2011 at 16:24 | |||||
| Jan 19, 2011 at 16:08 | answer | added | Homology | timeline score: 30 | |
| Jan 19, 2011 at 15:43 | answer | added | Nate Eldredge | timeline score: 7 | |
| Jan 19, 2011 at 15:39 | vote | accept | Rostyslav Kravchenko | ||
| Jan 19, 2011 at 15:39 | |||||
| Jan 19, 2011 at 15:35 | vote | accept | Rostyslav Kravchenko | ||
| Jan 19, 2011 at 15:35 | |||||
| Jan 19, 2011 at 14:45 | answer | added | Mikael de la Salle | timeline score: 7 | |
| Jan 19, 2011 at 12:59 | history | edited | Rostyslav Kravchenko |
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| Jan 19, 2011 at 12:50 | history | asked | Rostyslav Kravchenko | CC BY-SA 2.5 |