Timeline for What is the smallest $C^*$-algebra containing the "standard" pseudodifferential operators?
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 20, 2011 at 20:46 | answer | added | Bob Yuncken | timeline score: 4 | |
| Aug 31, 2010 at 1:52 | vote | accept | Otis Chodosh | ||
| Aug 30, 2010 at 23:01 | answer | added | Paul Siegel | timeline score: 6 | |
| Aug 30, 2010 at 4:04 | comment | added | Otis Chodosh | Thanks! I've edited the question to take your remarks into account. | |
| Aug 30, 2010 at 4:03 | history | edited | Otis Chodosh | CC BY-SA 2.5 |
changed question to have a higher chance of having an answer, per Yemon Choi's comments
|
| Aug 30, 2010 at 3:29 | comment | added | Yemon Choi | From MR90d:47016 (Gramsch, Kaballo, IEOT 1989) "Some of the main tools used by the authors are the so-called $\Psi$- and $\Psi^*$-algebras, for which an appropriate analytic perturbation theory holds (they are Fréchet algebras with an open group of invertible elements and continuous inversion). We mention that many algebras of pseudodifferential operators are $\Psi$-algebras." | |
| Aug 30, 2010 at 3:25 | comment | added | Yemon Choi | I'm aware that my comment isn't helpful in terms of answering the original question; I'll try to come back later with either references or an actual calculation | |
| Aug 30, 2010 at 3:23 | comment | added | Yemon Choi | My extremely hazy recollection is that $\Psi^0$ is not norm-closed in ${\mathcal L}(L^2)$, and that there is no reasonable topology to put on the latter to make $\Psi^0$ closed therein. Very roughly, think of Schwarz functions inside $L^2(R)$ - the former are naturally a Frechet space, the latter is naturally a Banach space, and as far as I know no good has come of trying to change the topology on either to make it fit better with the other. | |
| Aug 30, 2010 at 2:41 | history | asked | Otis Chodosh | CC BY-SA 2.5 |