Timeline for When is a Pseudo-differential operator trace class or in Dixmier ideal?

11 events

when toggle format	what		by	license	comment
S Jan 15, 2018 at 9:18	history	suggested	Ali Taghavi		I add a tag
Jan 15, 2018 at 7:39	review	Suggested edits
S Jan 15, 2018 at 9:18
Jan 28, 2013 at 17:24	comment	added	Asghar Ghorbanpour		Thanks for the useful references. However, I still wondering if there is a bound like $l$ such that pseudo differential operator of the order $d$ is in the Dixmier ideal (not necessary measurable) when $d<l$. of course $l$ should be in $[-k,0)$ where $k=dim M$.
Jan 28, 2013 at 10:30	comment	added	Branimir Ćaćić		Moreover, by the Connes trace formula (alainconnes.org/docs/action88.pdf), if your operator is of order $-k$ for $k = \dim M$, then it is in the Dixmier ideal; indeed, it is measurable (in the sense of the theory of Dixmier traces), and the (unique value of the) Dixmier trace is given by the Wodzicki residue of your operator.
Jan 28, 2013 at 5:09	history	edited	Otis Chodosh		edited tags
Jan 28, 2013 at 5:06	answer	added	Rafe Mazzeo		timeline score: 6
Jan 28, 2013 at 4:22	history	edited	Asghar Ghorbanpour	CC BY-SA 3.0	edited title
Jan 27, 2013 at 11:33	answer	added	Bazin		timeline score: 5
Jan 26, 2013 at 21:53	history	edited	Asghar Ghorbanpour	CC BY-SA 3.0	edited title
Jan 26, 2013 at 14:43	comment	added	Liviu Nicolaescu		It is trace class when it is an operator of order $-k$, $k>\dim M$. For a proof see Section 4.3 of these notes www3.nd.edu/~lnicolae/Pseudo.pdf
Jan 25, 2013 at 23:46	history	asked	Asghar Ghorbanpour	CC BY-SA 3.0