Abstract Let G be a compact Lie group of dimension n. In this work we characterise the membership of classical pseudo-differential operators on G in the trace class ideal 𝒮 1 (L 2 (G) ) S₁ (L^{2 (G) ) }, as well as in the setting of the Schatten ideals 𝒮 r (L 2 (G) ) Sₑ (L^{2 (G) ) }, for all r > 0 r>0. In particular, we deduce Schatten characterizations of elliptic pseudo-differential operators of (ρ, δ) (, ) -type for the large range 0 ≤ δ ρ ≤ 1 0 G × G ^ {G, with the momentum variables belonging to the unitary dual G ^ G of G. In terms of the parameters (ρ, δ) (, ), on the torus 𝕋 n T^{n}, we demonstrate the sharpness of our results show
Cardona et al. (Tue,) studied this question.