A Semi-Classical Szegő-type Limit Theorem for Toeplitz Operators

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