Nuclear Pseudo-Differential Operators in Besov Spaces on Compact Lie Groups

In 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.