Schatten properties of commutators on twisted crossed products

In this talk, we study Fourier multiplier commutators on a twisted crossed product $M ⋊R^d$. We will characterise their Schatten $p$-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 $p$-class membership of these commutators by a Sobolev space. As an example, our results applied to noncommutative Euclidean Space.

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