Commutators of the Unilateral Shift and Adjoint for Reproducing Kernel Hilbert Spaces on the Disk

Abstract

We generalise the result of Berger and Shaw the trace formula for Hardy Hilbert space to a larger class of rotation invariant Hilbert function spaces on the unit disk. We also demonstrate many meaningful examples of these Hilbert spaces by computing the inner products. We also extend to a wider class than the unilateral shift, that is, weighted shifts under certain restrictions.