Schatten properties of commutators on twisted crossed products

In this talk, we study Fourier multiplier commutators on a twisted crossed product $\mathrm{<span\; style="font-family:"times\; new\; roman";">M</span>}<span\; style="font-family:"times\; new\; roman";"> ⋊</span>{\mathrm{<span\; style="font-family:"times\; new\; roman";">R</span>}}^{\mathrm{<span\; style="font-family:"times\; new\; roman";">d</span>}}$. We will characterise their Schatten $\mathrm{<span\; style="font-family:"times\; new\; roman";">p</span>}$-class membership by that of their symbols in the associated Besov space. In addition, we show a formula on the Dixmier trace, which also gives us a characterization of the weak Schatten $\mathrm{<span\; style="font-family:"times\; new\; roman";">p</span>}$-class membership of these commutators by a Sobolev space. As an example, our results applied to noncommutative Euclidean Space.

More information about the Analysis Seminar can be found here.