A Semi-Classical Szeg\H{o}-type Limit Theorem for Toeplitz Operators

We obtain Szeg\H o-type limit theorems for Toeplitz operators on the weighted Bergman spaces $A^{2}_{\alpha}(\mathbb{B}^{n})$, and on $L^{2}(G)$, presenting separate formulations for compact and locally compact Abelian groups. Furthermore, we establish a broad class of abstract Szeg\H{o} limit theorems that unify and extend many classical results.