Duván Cardona2026-03-222026-03-22201610.48550/arxiv.1610.09042https://doi.org/10.48550/arxiv.1610.09042https://andeanlibrary.org/handle/123456789/83942In this work we establish the metric approximation property for Besov spaces defined on arbitrary compact Lie groups. As a consequence of this fact, we investigate trace formulae for nuclear Fourier multipliers on Besov spaces. Finally, we study the r-nuclearity, the Grothendieck-Lidskii formula and the (nuclear) trace of pseudo-differential operators in generalized Hörmander classes acting on periodic Besov spaces. We will restrict our attention to pseudo-differential operators with symbols of limited regularity.enMathematicsLie groupPure mathematicsTRACE (psycholinguistics)Differential operatorDifferential (mechanical device)Metric (unit)Pseudo-differential operatorBesov spaceMicrolocal analysispreprint